Question

If the length of the chord of contact of the tangents to the parabola $y^{2}=4x$ drawn from a point $\left(\right.-3,2\left.\right)$ is $\lambda $ units, then the value of $\frac{\lambda ^{2}}{100}$ is

Answer 1

Equation of chord of contact is $y=x-3$
Taking intersection with $y^{2}=4x,$
$y^{2}=4\left(\right.y+3\left.\right)$
$\Rightarrow $ $y^{2}-4y-12=0$
$y=6ory=-2$
$x=9orx=1$
$\left(\right.9,6\left.\right)$ and $\left(\right.1,-2\left.\right)$ are the points of intersection
Length of the chord of contact = $\sqrt{64 + 64}=8\sqrt{2}$ units
Hence, $\lambda =8\sqrt{2}\Rightarrow \frac{\lambda ^{2}}{100}=\frac{128}{100}$