Question

The latusrectum of the parabola $y^2=4ax$ whose focal chord is $PSQ$ such that $SP=3$ and $SQ=2$ being focus, is given by

• A. $\frac{24}{5}$
• B. $\frac{12}{5}$
• C. $\frac{6}{5}$
• D. $\frac{1}{5}$

Answer 1

Answer: (A)

$\frac{24}{5}$

REF.Image.

PS = 3

PQ = 2

semi latus rectum is Harmonic mean of

segments of focal chord

$\therefore$ semi latus rectum =$\frac{2\times SP\times SQ}{SP+SQ}$

$=\frac{2\times 3\times 2}{2+3}=\frac{12}{5}$

latus rectum $=2\times \frac{12}{5}=\frac{24}{5}$