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If the normals at two points P and Q of a parabola y 2 =4ax intersect at a third point R on the curve then find the product of ordinates of P and Q.

If the normals at two points P and Q of a parabola y2=4ax intersect at a third point R on the curve then find the product of ordinates of P and Q.

Grade:12

2 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

y^2=4ax,2yy'=4a,y'=2a/y,slope of normal=-1/y' =-y/2a, equation of first normal=(y-y1)/(x-((y1)^2/4a))=-y1/2a,

2ay-2ay1=-y1x+((y1)3)/4a)... eq(1), 2ay-2ay2=-y2x+(((y2)^3)/4a) ...(2) solve the two previous simultaneous equations to obtain (X,Y) for the point of intersection. let Y^2=4aX, this will take you to the answer.  

ankitesh gupta
63 Points
8 years ago

 

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