Question

Prove that the lines joining the ends of latus rectum of the parabola $y^2=4ax$ with the point of intersection of its axis and directrix are at right angles.

Answer 1

Slope of $AB=\frac{(0-0)}{(0-a)}=0.$ ------ $\left(1\right)$

Slope of $CD=\frac{(2a+2a)}{a-a}=00$.

Hence $=\tan \theta =00.$

$\theta ={90}^o$ ------ $\left(2\right)$

Hence from $\left(1\right)$ and $\left(2\right)$ we have

$AB$ is perpenducular to $CD$