Question

What will be the equation of normal at a point $(4,-2)$ on the parabola $x^2=-8y$?

Answer 1

Given the parabola $x^2=-8y$ having $a=2$.
Equation of normal at any point $(x_1,y_1)$ to the parabola $y^2=4ax$ is given by $(y-y_1)=\frac{2a}{x_1}(x-x_1).$
So, according to question equation of normal is,
$\Rightarrow y+2=\frac{4}{4}(x-4)$
$\Rightarrow x-y=6$
Hence, the equation of normal to parabola to the point $(4,-2)$ is $x-y=6.$