Q. The length of the latusrectum of the parabola whose focus is $(3,3)$ and directrix is $3x - 4y - 2 = 0,\$is
A) 2
B) 1
C) 4
D) None of these
Explanation
(a)
Since, the distance between the focus and directrix of the parabola is half of the length of the latusrectum. Therefore length of latusrectum =2 (length of the perpendicular from $(3,\ 3)$ to $3x - 4y - 2 = 0$)
$= 2\left| \frac{9 - 12 - 2}{\sqrt{9 + 16}} \right| = 2 \bullet \frac{5}{5} = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.