Question

The latus rectum of a parabola 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. $\frac{48}{5}$

Answer 1

The correct option is A $\frac{24}{5}$

Given, $SP=3$

$SQ=2$

By property of parabola

The harmonic mean of the lengths two parts into which the focus divides the focal chord is equal to length of semi-latus rectum.

Let length of lotus rectum be L

$\frac{2SP\times SQ}{SP+SQ}=\frac{1}{2}$

$L=\frac{4\times SP\times SQ}{SP+SQ}=\frac{4\times 3\times 2}{3+2}=\frac{24}{5}$.