Q. The number of distinct normals that can be drawn to parabola $y^{2} = 16x$ from the point $(2,\ 0)$, is
A) 1
B) 2
C) 3
D) 0
Explanation
(a)
The equation of normal is
$y = mx - 8m - 4m^{3}\ \ \ \ \ (\because y = mx - 2am - am^{3})$
Since, it is passing through $(2,\ 0)$
$\therefore 0 = 2m - 8m - 4m^{3}$
$\Rightarrow m = 0$ and $2m^{2} = - 3$ (no real value exist)
Only one real value of $m$ exist
$\therefore$ One normal can be drawn
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.