Question

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

Answer 1

Answer: 1.28

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