Question

The chord of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to the parabola $y^2=-4x$ passes through fixed point

• A. $(-2,1)$
• B. $(-2,-1)$
• C. $(1/2,1/4)$
• D. $(-1/2,-1/4)$

Answer 1

The correct option is A $(-2,1)$

The chord of contact of pair of tangent drawn from each point on the line $2x+y=4$ to the parabola $y^2=-4x$ passes through fixed point

Let $(h,k)$ be the point

$(h,k)$ satisfies $2x+y=4$

$2h+k=\mathrm{4............}\left(1\right)$

For parabola $y^2=-4x$

Chord of contact is

$ky=-2x-2h$

$2x+ky=-2h..........\left(2\right)$

(1) and (2) represent same line

$\frac{1}{k}=-\frac{4}{-2h}=1$

So, $h=-2,k=1$

Point is $(-2,1)$