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