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Question

Let from any point P on the line y=x, two tangents are drawn to the circle (x2)2+y2=1. Then the chord of contact of P with respect to given circle always passes through a fixed point, whose coordinates are given by

A
(32,14)
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B
(32,14)
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C
(32,12)
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D
(32,12)
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Solution

The correct option is D (32,12)
Given equation of the circle :
(x2)2+y2=1x2+y24x+3=0

Let (a,a) be any point on line y=x.
Chord of contact of this point w.r.t. circle is
ax+ay42(x+a)+3=0
a(x+y2)+(32x)=0
which always passes through the intersection of the lines x+y2=0 and 32x=0, which is given by(32,12)

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