Question

The number of normals drawn to the parabola $y^2 = 4x$ from the point $(1, 0)$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (B)

Equation of normal to parabola $y ^{2}=4 ax$ in slope form is
$y=m x-2 a m-a m^{3}$
For the given parabola $a =1$
So, the equation of normal is
$y = mx -2 m - m ^{3}$
The normal passes through the point $(1,0)$
$\therefore 0=m(1)-2 m-m^{3} $
$\therefore m^{3}+m=0$
$\therefore m =0$ is the only solution.
So, only one normal can be drawn from the point $(1,0)$