Question

The line $ x = my + c $ is normal to $ x^2 = - 4ay $ , if $c$ is equal to

• A. $ - 2 am - m^3 a $
• B. $ - 2 am + am^3 $
• C. $ - 2 am - am^3 $
• D. $ 2 am + am^3 $

Answer 1

Answer: (D)

We know that equation of normal to the parabola $x^{2}=-4 a y$ in the slope form is
$x=m y+2 a m+a m^{3}$
and point of contact is $\left(2 a m,-a m^{2}\right)$
So, line $x=m y+c$ is normal to $x^{2}=-4 a y$
if $c=2 a m+a m^{3}$