Q. In the parabola $y^{2} = 4ax$, the length of the chord passing through the vertex inclined to the axis at $\frac{\pi}{4}$ is
A) $4a\sqrt{2}$
B) $2a\sqrt{2}$
C) $a\sqrt{2}$
D) $a$
Explanation
(a)
Equation of line which is inclined to the axis at $\frac{\pi}{4}$ is $y = x$
The point of intersection of above line and given parabola is (0,0), $(4a,\ 4a)$
Length of the chord is $= \sqrt{(4a - 0)^{2} + (4a - 0)^{2}} = 4a\sqrt{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.