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Analytical Geometry

Scorching goIITian

Joined:	19 Aug 2008
Post:	219

31 Aug 2008 18:07:46 IST

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524

problem on parabola

None

if the point of intersection of normals at points A and B of a parabola y²= 4ax lies on the line y+a=0, then the point of intersection of the tangents at A and B lie on

x+a=o

xy=a²

x²-y²=a²

x²+y²=a²

^{PLSE SOMEONE SOLVE THIS QUESTION}

RATES 4 SURE!

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Comments (1)

anchit saini

Blazing goIITian

Joined: 1 Feb 2008

Posts: 1251

31 Aug 2008 18:31:42 IST

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$\mbox{Point of intersection of normals (y) =}-at_1t_2(t_1 + t_2) \\ \\ =-a \ \mbox{given as it lies on y=-a} \\ \\ \mbox{Hence , }t_1t_2(t_1 + t_2)=1 \\ \\ \mbox{Also,pt of intersection of tangents is }-> \\ \\ x= at_1t_2 \\ \\ y= a(t_1 + t_2) \\ \\ Thus, -> xy=a^2t_1t_2(t_1 + t_2)=a^2$

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