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