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The point of intersection of the tangent...

The point of intersection of the tangents of the parabola `y^2=4x` drawn at the endpoints of the chord `x+y=2` lies on
(a)`x-2y=0` (b) `x+2y=0` (c)`y-x=0` (d) `x+y=0`

A

x-2y=0

B

x+2y=0

C

y-x=0

D

x+y=0

Text Solution

Verified by Experts

The correct Answer is:
C
(3) Let the point of intersection be `(alpha,beta)`.
Therefore, the chord of contact w.r.t. this point is
`betay=2x+aalpha`
which is the same as x+y=2. Therefore,
`alpha=beta=-2`
These value satisfy y-x=0.
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