Q.

If the chords of contact of P(x1, y1) and Q(x2, y2) w.r.t the ellipse x2a2+y2b2=1 are at right angle then x1 x2y1 y2=

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a

-b2a2

b

-b4a4

c

-a4b4

d

a2b2

answer is C.

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Detailed Solution

Given ellipse isx2a2+y2b2=1

equation  of chord of contact of P(x1,y1) is

x x1a2+y y1b2=1

slope of line m1=-b2x1a2y1

equation  of chord of contact of P(x2,y2) is

x x2a2+y y2b2=1

slope of line m2=-b2x2a2y2

m1m2=-1 b4 x1x2a4×y1y2=-1 x1 x2y1 y2=-a4b4 

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