Question

The chords of contact of the pairs of tangents drawn from each point on the line $2x+y=4$ to the parabola $y^2=-4x$ pass through the point

• A. $(2,-1)$
• B. $(\frac{1}{2},\frac{1}{4})$
• C. $(-\frac{1}{2},-\frac{1}{4})$
• D. $(-2,1)$

Answer 1

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

Let $P(t,4-2t)$ be any point on $2x+y=4$.

The chord of contact of tangents drawn from $P$ to $y^2=-4x$ is
$(4-2t)y=-2(x+t)$

$\Rightarrow (2x+4y)-2t(y-1)=0$
Clearly, it represents a line passing through the point of intersection of the line $2x+4y=0$ and $y-1=0$ i.e.$(-2,1)$.