Q. The angle made by a double ordinate of length $8a$ at the vertex of the parabola $y^{2} = 4ax$ is
A) $\frac{\pi}{3}$
B) $\frac{\pi}{2}$
C) $\frac{\pi}{4}$
D) $\frac{\pi}{6}$
Explanation
(b)
Given equation of parabola is $y^{2} = 4ax$. Since, $AB = 8a,$ it means ordinate of $A$ and $B$ respectively $4a$ and $- 4a$. General point on this parabola is $\left( {at}^{2},\ 2at \right) \Rightarrow t = \pm 2$
[image:11_image61.emf]
So, ${at}^{2} = 4a$
$\therefore OM = 4a,\ AM = 4a$
So, $\angle AOM = 45{^\circ}$
$\therefore$ The angle $AOB$ is $90{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.