Q. The latusrectum of the parabola $y^{2} = 4ax$ whose focal chord is $PSQ$ such that $SP = 3$ and $SQ = 2$, is given by
A) $\frac{24}{5}$
B) $\frac{12}{5}$
C) $\frac{6}{5}$
D) $\frac{1}{5}$
Explanation
(a)
Since, the semi-latusrectum of a parabola is HM of segments of a focal chord
$\therefore$ Semi-latusrectum $= \frac{2SP \bullet SQ}{SP + SQ} = \frac{2 \times 3 \times 2}{3 + 2} = \frac{12}{5}$
$\Rightarrow$ Latusrectum of the parabola =2$\times$ semi-latusrectum
$= \frac{24}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.