Question

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

• A. 24/5
• B. 12/5
• C. 6/5
• D. 1/5

Answer 1

Answer: (A)

Key Idea : Since the semi-latus rectum of a parabola is the HM of segments of a focal chord.
$\therefore$ Semi-latus rectum $=\frac{2SP\cdot SQ}{SP+SQ}$
$=\frac{2\times 3\times 2}{3+2}=\frac{12}{5}$
$\therefore$ Latus rectum of the parabola $=\frac{24}{5}$.