Question

The point $(3,4)$ is the focus and $2x-3y+5=0$ is the directrix of a parabola. Lenghth of latus rectum is

• A. $\frac{2}{\sqrt{13}}$
• B. $\frac{4}{\sqrt{13}}$
• C. $\frac{1}{\sqrt{13}}$
• D. $\frac{3}{\sqrt{13}}$

Answer 1

The correct option is A $\frac{2}{\sqrt{13}}$

We know that, Latus rectum $=2\times$ (distance from focus to directrix)
$=2\cdot \frac{|6-12+5|}{\sqrt{4+9}}=\frac{2}{\sqrt{13}}$