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)
Since, focal chord of parabola $y^{2} = ax$ is $2x - y - 8 = 0$
$\because$ This chord passes through focus $ie,\ \left( \frac{a}{4},\ 0 \right)$
$\therefore 2 \bullet \frac{a}{4} - 0 - 8 = 0$
$\Rightarrow a = 16$
$\therefore$ 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.