{"id":3933,"date":"2021-01-30T12:25:26","date_gmt":"2021-01-30T12:25:26","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3933"},"modified":"2023-06-22T17:41:00","modified_gmt":"2023-06-22T11:41:00","slug":"equation-of-parabola","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/equation-of-parabola\/","title":{"rendered":"\u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (Equation of Parabola Passing through origin)"},"content":{"rendered":"

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4 (<\/b>Parabola) : <\/b>\u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (<\/b>Equation of Parabola Passing through origin):<\/b><\/h2>\n

\u09a7\u09b0\u09bf, \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <\/span>S<\/span>, \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be <\/span>M Z M^{\\prime}<\/span><\/span>\u0964<\/span><\/p>\n

M Z M^{\\prime}<\/span><\/span> \u098f\u09b0 \u0989\u09aa\u09b0 <\/span>S Z<\/span><\/span> \u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09bf \u098f\u09ac\u0982 S Z<\/span><\/span>\u00a0\u0995\u09c7 <\/span>A<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u09bf\u09a4 \u0995\u09b0\u09bf\u0964<\/span><\/p>\n

\u09a4\u09be\u09b9\u09b2\u09c7, <\/span>A<\/span><\/span> \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0<\/span>\u00a0<\/span> \u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u098f\u09ac\u0982 \u09b6\u09c0\u09b0\u09cd\u09b7 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0964<\/span><\/p>\n

Z S X<\/span><\/span> \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u099f\u09bf\u09b0 \u0985\u0995\u09cd\u09b7\u09b0\u09c7\u0996\u09be\u0964<\/span><\/p>\n

\u09a7\u09b0\u09bf, \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>P(x, y)<\/span><\/span> \u098f\u09ac\u0982<\/span>\u00a0<\/span>Z A=A S=a<\/span> <\/span>\u0964<\/span><\/p>\n

P<\/span><\/span>\u00a0 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09c7\u09b0 \u0993\u09aa\u09b0 <\/span>P M<\/span>\u00a0<\/span> \u0993\u00a0 <\/span>A X<\/span><\/span> \u098f\u09b0 \u0993\u09aa\u09b0 <\/span>P N<\/span><\/span> \u09b2\u09ae\u09cd\u09ac \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09bf\u0964 <\/span>S, P<\/span><\/span> \u09af\u09cb\u0997 \u0995\u09b0\u09bf\u0964\"Graph<\/span>\u2234<\/span> \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \\therefore<\/span> \u09ab\u09cb\u0995\u09be\u09b8 S(a, 0)<\/span><\/span><\/p>\n

\u00a0<\/span>\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987, \\frac{S P}{P M}=e=1<\/span><\/span><\/p>\n\\begin{array}{l}\n\n\\Rightarrow S P=P M \\\\\n\n\\Rightarrow S P=Z N \\\\\n\n\\Rightarrow S P=A Z+A N \\\\\n\n\\Rightarrow S P=a+x\n\n\\end{array}<\/span>\n

\\Rightarrow S P^{2}=(a+x)^{2}<\/span><\/span><\/p>\n

\\Rightarrow(x-a)^{2}+(y-0)^{2}=(a+x)^{2}<\/span><\/span><\/p>\n

\\Rightarrow y^{2}=(x+a)^{2}-(x-a)^{2}<\/span><\/span><\/p>\n

\\therefore y^{2}=4 a x<\/span><\/span><\/p>\n

\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09b2\u09cb \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0986\u09a6\u09b0\u09cd\u09b6 \u09ac\u09be \u09aa\u09cd\u09b0\u09ae\u09bf\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (Standard Equation)\u0964<\/span><\/p>\n

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u0985\u0999\u09cd\u0995\u09a8: y^{2}=4 a x<\/span><\/span><\/b>\u00a0<\/b>(Graphic the parabola y^{2}=4 a x<\/span><\/span><\/b><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, y^{2}=4 a x ; a>0<\/span><\/span>\u00a0<\/span>\u00a0<\/span>\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <\/span>S<\/span> \u098f\u09ac\u0982 \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be <\/span>MM’<\/span><\/p>\n

\u09a8\u09bf\u09df\u09be\u09ae\u0995\u09c7\u09b0 \u0989\u09aa\u09b0 <\/span>SZ<\/span> \u09b2\u09ae\u09cd\u09ac \u0986\u0981\u0995\u09bf\u0964<\/span><\/p>\n

\u098f\u09ac\u0982 <\/span>SZ<\/span> \u0995\u09c7 <\/span>A<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u09bf\u09a4 \u0995\u09b0\u09bf\u0964<\/span><\/p>\n

\\therefore S Z = A Z<\/span><\/span>\u00a0<\/span><\/p>\n

\u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, \\frac{S A}{A Z}=1<\/span><\/span><\/p>\n

\u0985\u0999\u09cd\u0995\u09a8:<\/b><\/p>\n

\"Graph<\/p>\n

\u09e7) \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0993\u09aa\u09b0 <\/span>A<\/span><\/span> \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09ac\u09b0\u09cd\u09a7\u09bf\u09a4 <\/span>A S<\/span><\/span> \u098f\u09b0 \u0989\u09aa\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>N<\/span><\/span> \u09a8\u09bf\u0987 \u0993 <\/span>Z S \\perp P P^{\\prime}<\/span><\/span> \u0986\u0981\u0995\u09bf\u0964<\/span><\/p>\n

\u09e8) S<\/span><\/span>\u00a0\u0995\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u09b0\u09c7 <\/span>Z N<\/span><\/span> \u098f\u09b0 \u09b8\u09ae\u09be\u09a8 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09a8\u09bf\u09df\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u099a\u09be\u09aa \u0986\u0981\u0995\u09bf \u09af\u09c7\u09a8 \u09a4\u09be <\/span>P N P^{\\prime}<\/span><\/span> \u0995\u09c7 <\/span>P<\/span><\/span> \u0993 <\/span>P^{\\prime}<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u099b\u09c7\u09a6 \u0995\u09b0\u09c7\u0964<\/span>\u00a0<\/span><\/p>\n

\u09e9) \u098f\u0996\u09a8, \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09c7\u09b0 \u0993\u09aa\u09b0 <\/span>P M<\/span><\/span> \u0993 P^{\\prime} M^{\\prime}<\/span><\/span> \u09b2\u09ae\u09cd\u09ac \u0986\u0981\u0995\u09bf\u0964 \u09ab\u09b2\u09c7, <\/span>S P=Z N=P M<\/span><\/span><\/p>\n

\/therefore<\/span><\/span> \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0993\u09aa\u09b0 <\/span>P<\/span><\/span> \u098f\u0995\u099f\u09bf<\/span>\u00a0<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0964<\/span><\/p>\n

\u09ea) \u098f\u0995\u0987\u09ad\u09be\u09ac\u09c7, <\/span>A S<\/span><\/span> \u098f\u09b0 \u0993\u09aa\u09b0 N_1, N_2<\/span><\/span>\u2026\u2026<\/span> \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09bf\u09df\u09c7 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0<\/span>\u00a0<\/span>\u0993\u09aa\u09b0 Q, Q^{\\prime} ; R, R^{\\prime}<\/span> <\/span>\u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/span>\u00a0<\/span>\u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df\u0964<\/span>\u00a0<\/span><\/p>\n

\u09eb) \u098f\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09c1\u09b2\u09bf \u098f\u0995\u099f\u09bf \u09b8\u09c1\u09b7\u09ae \u09ac\u0995\u09cd\u09b0\u09b0\u09c7\u0996\u09be \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09af\u09cb\u0997 \u0995\u09b0\u09b2\u09c7 \u098f\u0995\u099f\u09bf \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df\u0964<\/span><\/p>\n

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09bf\u0995 \u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af<\/b> (Length of the epicenter perpendicular to the parabola)<\/b>:<\/b><\/h3>\n

\"\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0<\/p>\n

y^{2}=4 a x<\/span>\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0,<\/span>\u00a0<\/span><\/p>\n

\u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <\/span>S<\/span>, \u09a8\u09bf\u09df\u09be\u09ae\u0995\u00a0 <\/span>MZM’<\/span>,<\/span><\/p>\n

\u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>A<\/span>, \u0985\u0995\u09cd\u09b7\u00a0 <\/span>ZS<\/span> \u098f\u09ac\u0982<\/span><\/p>\n

\u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09bf\u0995 \u09b2\u09ae\u09cd\u09ac <\/span>LSL’ <\/span>\u0964<\/span>\u00a0<\/span><\/p>\n

\u09a4\u09be\u09b9\u09b2\u09c7, <\/span>S<\/span> \u098f\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995<\/span>\u00a0<\/span>(a,\u00a00)<\/span><\/p>\n

LM \u22a5 MM’<\/span> \u09b9\u09b2\u09c7,<\/span><\/p>\n

SL = LM= ZS =AZ + AS<\/span>\u00a0<\/span><\/p>\n

\u00a0 <\/span>= a + a= 2a<\/span><\/p>\n

\u2234L<\/span>L<\/span>‘<\/span>= SL + SL<\/span>\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>=2a + 2a= 4a<\/span><\/p>\n

\u2234<\/span> \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09bf\u0995 \u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <\/b>= |4a|<\/span><\/p>\n

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09bf\u0995 \u09b2\u09ae\u09cd\u09ac\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af<\/span>\u00a0<\/span>=2\u00d7<\/span> \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span>\u00a0<\/span><\/p>\n

=4\u00d7<\/span> \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/span>\u00a0<\/span>\u0993 \u09ab\u09cb\u0995\u09be\u09b8\u09c7\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span>\u00a0<\/span><\/p>\n

=4\u00d7<\/span> \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span><\/p>\n

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0993 \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u098f\u09ac\u0982 \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3: (y^{2}=4 a x<\/span><\/b>) <\/b>(The vertex of the parabola, Coordinates of the epicenter, Equilibrium of the control line)<\/b><\/h3>\n

\"The<\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf,y^{2}=4 a x ; a>0<\/span><\/span>\u00a0\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <\/span>S<\/span> \u098f\u09ac\u0982 \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be <\/span>MZM’<\/span>\u0964 <\/span>MZM’<\/span> \u098f\u09b0 \u0989\u09aa\u09b0 <\/span>SZ<\/span> \u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09bf \u098f\u09ac\u0982 <\/span>SZ<\/span> \u0995\u09c7 <\/span>A<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u09bf\u09a4 \u0995\u09b0\u09bf\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 <\/span>A<\/span> \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0964 \u09a7\u09b0\u09bf, <\/span>XAX’<\/span> \u0993 <\/span>YAY’<\/span> \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>x<\/span> \u0985\u0995\u09cd\u09b7 \u0993 <\/span>y<\/span> \u0985\u0995\u09cd\u09b7\u0964<\/span><\/p>\n

\u09a4\u09be\u09b9\u09b2\u09c7 \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>A<\/span> \u098f\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 <\/span>(0,0)<\/span><\/p>\n

AS = a<\/span> \u09b9\u09b2\u09c7 <\/span>ZA = a<\/span> \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u2234<\/span>\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 <\/span>S(a,\u00a00)<\/span> \u098f\u09ac\u0982 \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be\u09b0 \u09aa\u09be\u09a6\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 <\/span>Z (-a, 0)<\/span>\u0964 <\/span>y<\/span> \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u0993 <\/span>Z(-a,\u00a00)<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be <\/span>MZM’<\/span> \u098f\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/span><\/p>\n

\u00a0 <\/span>x=-a<\/span><\/p>\n

\u21d2x+a=0<\/span><\/p>\n

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/b>\u00a0<\/b>\\boldsymbol{\\alpha}, \\boldsymbol{\\beta}<\/span><\/span> \u098f\u09ac\u0982 \u0985\u0995\u09cd\u09b7\u09b0\u09c7\u0996\u09be <\/b>x<\/span><\/span> \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09b2\u09c7 \u098f\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/b>\u00a0 (\\boldsymbol{y}-\\boldsymbol{\\beta})^{2}=4 \\boldsymbol{a}(\\boldsymbol{x}-\\boldsymbol{\\alpha})<\/span><\/h3>\n

\"\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0<\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf,<\/span>\u00a0<\/span>\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>A (\u03b1,\u03b2)<\/span> \u098f\u09ac\u0982 <\/span>ZA = AS = a<\/span><\/p>\n

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u099f\u09bf\u09b0 \u0985\u0995\u09cd\u09b7\u09b0\u09c7\u0996\u09be <\/span>x<\/span> \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2\u0964<\/span>\u00a0<\/span><\/p>\n

\u2234<\/span> \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u099f\u09bf\u09b0 \u09ab\u09cb\u0995\u09be\u09b8 <\/span>S (\u03b1+a, \u03b2)<\/span> \u098f\u09ac\u0982 \u09a8\u09bf\u09df\u09be\u09ae\u0995 \u09b0\u09c7\u0996\u09be\u09b0 \u09aa\u09be\u09a6\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/span>\u00a0<\/span>Z(\u03b1-a,\u00a0\u03b2)<\/span><\/p>\n

\u2234<\/span> \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>x = \u03b1 – a\u00a0<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span>\u21d2 x – \u03b1 + a = 0<\/span><\/p>\n

\u2234<\/span> \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3: \\{x-(\\alpha+a)\\}^{2}+(y-\\beta)^{2}=(x-\\alpha+a)^{2}<\/span><\/span><\/p>\n\\Rightarrow\\{x-(\\alpha+a)\\}^{2}+(y-\\beta)^{2}=\\{x-(\\alpha-a)\\}^{2}<\/span>\n

(\\Rightarrow(y-\\beta)^{2}=\\{x-(\\alpha-a)\\}^{2}-\\{x-(\\alpha+a)\\}^{2}<\/span><\/span><\/p>\n

\\Rightarrow(y-\\beta)^{2}=(x-a+a+x-a-a)(x-a+a-x+a+a)<\/span><\/span><\/p>\n\\Rightarrow(y-\\beta)^{2}=2(x-\\alpha) \\cdot 2 a<\/span>\n\\therefore(y-\\beta)^{2}=4 a(x-\\alpha)<\/span>\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b6\u09b0\u09cd\u09a4\u09be\u09a8\u09c1\u09af\u09be\u09df\u09c0 \u0987\u09b9\u09be\u0987 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964<\/span><\/p>\n

\u098f\u0996\u09a8, (y-\\beta)^{2}=4 a(x-\\alpha)<\/span><\/span><\/p>\n\\Rightarrow y^{2}-2 \\beta y+\\beta^{2}=4 a x-4 a \\alpha<\/span>\n

\\Rightarrow 4 a x=y^{2}-2 \\beta y+\\beta^{2}+4 a \\alpha<\/span> <\/span><\/p>\n\\Rightarrow x=\\frac{1}{4 a} y^{2}+\\left(\\frac{-\\beta}{2 a}\\right) y+\\frac{\\beta^{2}+4 a \\alpha}{4 a}<\/span>\n

\u2234 x<\/span>\u00a0 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u098f\u09b0\u09c2\u09aa \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/span> <\/span><\/span><\/p>\n

\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7, \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/span>\u00a0<\/span>(\u03b1,\u03b2)<\/span> \u098f\u09ac\u0982 \u0985\u0995\u09cd\u09b7\u09b0\u09c7\u0996\u09be <\/span>y<\/span> \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09b2\u09c7 \u098f\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/span>\u00a0\u00a0<\/span> x=a y^{2}+b y+c<\/span><\/p>\n

\u2234 y<\/span> \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u098f\u09b0\u09c2\u09aa \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/span> y=a x^{2}+b x+c<\/span><\/span><\/p>\n

\\bf y^{2}<\/span> = 4ax \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u00a0 y = mx+c \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u099f\u09bf \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4<\/strong><\/h3>\n

\"y2=4ax\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, y^{2}=4 a x \\ldots \\ldots(i)<\/span><\/span><\/p>\n

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u09b0 <\/span>P<\/span> \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u098f\u09ac\u0982 <\/span>PQ<\/span> \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u099b\u09c7\u09a6\u0995 \u099c\u09cd\u09af\u09be\u0964 <\/span>Q<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0995\u09cd\u09b0\u09ae\u09b6 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09a6\u09bf\u0995\u09c7 \u0985\u0997\u09cd\u09b0\u09b8\u09b0 \u09b9\u09df\u09c7 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u0989\u09aa\u09b0 \u09b8\u09ae\u09be\u09aa\u09a4\u09bf\u09a4 \u09b9\u09b2\u09c7 \u099b\u09c7\u09a6\u0995\u099f\u09bf<\/span>\u00a0<\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0989\u0995\u09cd\u09a4 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>PQ<\/span> \u099b\u09c7\u09a6\u0995\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u00a0<\/span><\/p>\n

y=mx+c\u2026\u2026(ii)<\/p>\n

(i)<\/span> \u0993 <\/span>(ii)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span>\u00a0<\/span><\/p>\n(m x+c)^{2}=4 a x<\/span>\n

m^{2} x^{2}+2(m c-2 a) x+c^{2}=0<\/span> <\/span><\/p>\n

PQ<\/span> \u099b\u09c7\u09a6\u0995 <\/span>(i)<\/span> \u09a8\u0982 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf <\/span>(iii)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09df \u09b8\u09ae\u09be\u09a8 \u09b9\u09df\u0964<\/span><\/p>\n

\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09df \u09b8\u09ae\u09be\u09a8 \u09b9\u09b2\u09c7 \u098f\u09b0 \u09aa\u09c3\u09a5\u09be\u09df\u0995 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09ac\u09c7, \u0985\u09b0\u09cd\u09a5\u09be\u09ce 4(m c-2 a)^{2}-4 m^{2} c^{2}=0<\/span><\/span><\/p>\n\\Rightarrow 4 m^{2} c^{2}-4.2 . m c .2 a+4.4 a^{2}-4 m^{2} c^{2}=0<\/span>\n\\Rightarrow 16 a^{2}-16 m c a=0\\\\<\/span>\n\\Rightarrow a^{2}-m c a=0<\/span>\n\\Rightarrow a-m c=0<\/span>\n\\Rightarrow m c=a<\/span>\n\\therefore c=\\frac{a}{m}<\/span>\n

\u2234y = mx + c<\/span> \u09b0\u09c7\u0996\u09be y^{2}=4 a x<\/span><\/span> \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u0995\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09ac\u09c7 \u09af\u09a6\u09bf c=\\frac{a}{m}<\/span> <\/span>\u09b9\u09df\u0964<\/span>\u00a0<\/span><\/p>\n

(iii)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 c=\\frac{a}{m}<\/span><\/span>\u00a0\u09ac\u09b8\u09bf\u09df\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\nm^{2} x^{2}+2\\left(m \\cdot \\frac{a}{m}-2 a\\right) x+\\left(\\frac{a}{m}\\right)^{2}=0<\/span>\n\\Rightarrow\\left(m x-\\frac{a}{m}\\right)^{2}=0<\/span>\n\\Rightarrow m x=\\frac{a}{m}<\/span>\n\\therefore x=\\frac{a}{m^{2}}<\/span>\n

\u2234y=mx+c<\/span>\u00a0<\/span><\/p>\n\\Rightarrow y=m\\left(\\frac{a}{m^{2}}\\right)+\\frac{a}{m}<\/span>\n

\u00a0 \u00a0\\Rightarrow\\frac{a}{m}+\\frac{a}{m}=\\frac{2 a}{m}<\/span><\/span><\/p>\n

\u2234<\/span> \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \\left(\\frac{a}{m^{2}}, \\frac{2 a}{m}\\right)<\/span><\/span><\/p>\n

\u2234y=mx+c<\/span> \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u099f\u09bf y^{2}=4 a x<\/span><\/span>\u00a0\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u0995\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09b2\u09c7 <\/span>c=\\frac{a}{m}<\/span><\/span>\u00a0\u09b9\u09ac\u09c7\u0964 \u0985\u09a4\u098f\u09ac, <\/span>m<\/span> \u098f\u09b0 <\/span>(m\u22600)<\/span> \u09b8\u0995\u09b2 \u09ae\u09be\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af y=m x+\\frac{a}{m}<\/span><\/span> \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u099f\u09bf y^{2}=4 a x<\/span><\/span>\u00a0\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u0995\u09be\u09b6<\/span>\u00a0<\/span>\u0995\u09b0\u09c7 \u098f\u09ac\u0982 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \\left(\\frac{a}{m^{2}}, \\frac{2 a}{m}\\right)<\/span><\/span>\u0964<\/span><\/p>\n

\u09a4\u09a6\u09cd\u09b0\u09c2\u09aa,<\/span> x^{2}=4 a y<\/span> <\/span>\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 y=m x-a m^{2}<\/span><\/span>\u0964 \u09af\u09c7\u0996\u09be\u09a8\u09c7, <\/span>c=-a m^{2}<\/span><\/span>\u00a0\u098f\u09ac\u0982 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995<\/span> =\\left(2 a m, a m^{2}\\right)<\/span><\/span><\/p>\n

\u09b8\u09ae\u09b8\u09cd\u09af\u09be (Problem):<\/b> \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, <\/span>lx+my+n=0<\/span> \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u099f\u09bf y^{2}=4 a x <\/span><\/span>\u00a0\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u0995\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09ac\u09c7 \u09af\u09a6\u09bf l n=a m^{2}<\/span><\/span>\u00a0\u09b9\u09df\u0964 <\/span> \u00a0 \u00a0 [\u09b0\u09be.\u2019\u09e6\u09eb; \u0995\u09c1.\u2019\u09e6\u09eb]<\/span><\/p>\n

\u09b8\u09ae\u09a7\u09be\u09a8 (Solution):<\/b> \u09a6\u09c7\u0993\u09df\u09be \u0986\u099b\u09c7, <\/span>lx + my + n = 0<\/span>\u00a0<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span>\u21d2 my= -l x -n<\/span>\u00a0<\/span><\/p>\n\\Rightarrow y=-\\frac{l x}{m}-\\frac{n}{m}<\/span>\n

\u098f\u09ac\u09be\u09b0, y=-\\frac{b x}{m}-\\frac{n}{m}<\/span><\/span>\u00a0\u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u099f\u09bf y^{2}=4 a x<\/span><\/span> \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u0995\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09be\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7, y=-\\frac{l x}{m}-\\frac{n}{m} \\cos y=m x+c<\/span><\/span>\u098f\u09b0 \u09b8\u09be\u09a5\u09c7 \u09a4\u09c1\u09b2\u09a8\u09be \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span>\u00a0<\/span><\/p>\nm=-\\frac{l}{m} \\text { \u098f\u09ac\u0982 } c=-\\frac{n}{m}<\/span>\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, c=\\frac{a}{m}<\/span><\/span><\/p>\n\\Rightarrow-\\frac{n}{m}=\\frac{a}{-\\frac{l}{m}}<\/span>\n\\Rightarrow-\\frac{n}{m}=-\\frac{a m}{l}<\/span>\n

\\Rightarrow l n=a m^{2}<\/span> (\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb)<\/b><\/p>\n

\u0985\u09a5\u09ac\u09be<\/b>, \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4 y^{2}=4 a x<\/span><\/span><\/p>\n

\u00a0 x=\\frac{y^{2}}{4 a} \\ldots \\ldots(i)<\/span><\/span><\/p>\n

\u098f\u09ac\u0982 \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be <\/span>lx + my + n = 0\u2026\u2026(ii)<\/span><\/p>\n

(i)<\/span> \u09a8\u0982 \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 <\/span>x<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 <\/span>(ii)<\/span> \u09a8\u0982 \u098f \u09ac\u09b8\u09bf\u09df\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/p>\nl \\cdot \\frac{y^{2}}{4 a}+m y+n=0<\/span>\n

\\Rightarrow \\frac{l y^{2}}{4 a} \\times 4 a+m y \\times 4 a+n \\times 4 a=0<\/span> [\u0989\u09ad\u09df\u09aa\u0995\u09cd\u09b7\u0995\u09c7 <\/span>4a<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0997\u09c1\u09a3 \u0995\u09b0\u09c7]<\/span><\/p>\n

\\Rightarrow l y^{2}+4 \\text { may }+4 n a=0<\/span>\u2026\u2026(iii)<\/span><\/p>\n

\u09af\u09be <\/span>y<\/span> \u098f\u09b0 \u098f\u0995\u099f\u09bf \u09a6\u09cd\u09ac\u09bf\u0998\u09be\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964<\/span>\u00a0<\/span><\/p>\n

\u2234(iii)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 <\/span>y<\/span> \u098f\u09b0 \u09a6\u09c1\u099f\u09bf \u09ae\u09be\u09a8 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7\u0964<\/span>\u00a0<\/span><\/p>\n

(ii)<\/span> \u09a8\u0982 \u09b0\u09c7\u0996\u099f\u09bf <\/span>(i)<\/span> \u09a8\u0982 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u0995\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09ac\u09c7 \u09af\u09a6\u09bf <\/span>y<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09ae\u09be\u09a8 \u09b9\u09df\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>(iii)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09a8\u09bf\u09b6\u09cd\u099a\u09be\u09df\u0995 \u09ac\u09be \u09aa\u09c3\u09a5\u09be\u09df\u0995 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09df\u0964 <\/span>(iii)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 b^{2}-4 a c=0<\/span> <\/span>\u098f\u09b0 \u09b8\u09be\u09a5\u09c7 \u09a4\u09c1\u09b2\u09a8\u09be \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n(4 m a)^{2}-4 . \\text { L. } 4 n a=0<\/span>\n\\Rightarrow 16 m^{2} a^{2}-16 n a l=0<\/span>\n\\Rightarrow m^{2} a-n l=0<\/span>\n

\\therefore \\ln =a m^{2}<\/span>\u00a0 \u00a0 \u00a0(\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb)<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4 (Parabola) : \u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (Equation of Parabola Passing through origin): \u09a7\u09b0\u09bf, \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 S, \u09a8\u09bf\u09df\u09be\u09ae\u0995\u09b0\u09c7\u0996\u09be \u0964 \u098f\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09bf \u098f\u09ac\u0982 \u00a0\u0995\u09c7 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u0996\u09a3\u09cd\u09a1\u09bf\u09a4 \u0995\u09b0\u09bf\u0964 \u09a4\u09be\u09b9\u09b2\u09c7, \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0\u00a0 \u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u098f\u09ac\u0982 \u09b6\u09c0\u09b0\u09cd\u09b7 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0964 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u099f\u09bf\u09b0 \u0985\u0995\u09cd\u09b7\u09b0\u09c7\u0996\u09be\u0964 \u09a7\u09b0\u09bf, \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0989\u09aa\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u099a\u09b2\u09ae\u09be\u09a8<\/p>\n

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