Q. If a focal chord of the parabola $y^{2} = ax$ is $2x - y - 8 = 0,$ then the equation of the directrix is
A) $x + 4 = 0$
B) $x - 4 = 0$
C) $y - 4 = 0$
D) $y + 4 = 0$
Explanation
(a)
Given focal chord of parabola $y^{2} = ax$ is $2x - y - 8 = 0$
Since, this chord passes through focus $\left( \frac{a}{4},0 \right)$
$\therefore\ 2.\frac{a}{4} - 0 - 8 = 0\ \Rightarrow \ a = 16$
Hence, directrix is $x = - 4\ \Rightarrow \ x + 4 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.