Question

Length of latus rectum of the parabola whose focus is at $(2,3)$ and directrix is the line $x–4y+3=0$ is

• A. $\frac{7}{\sqrt{17}}$
• B. $\frac{14}{\sqrt{17}}$
• C. $\frac{21}{\sqrt{17}}$
• D. $\frac{28}{\sqrt{17}}$

Answer 1

The correct option is B

$\frac{14}{\sqrt{17}}$

Distance between focus and directrix $=2a$

$\Rightarrow$ Distance between $(2,3)$ and $x–4y+3=0=\frac{|2-12+3|}{\sqrt{1+16}}=2a$

$\Rightarrow \frac{7}{\sqrt{17}}=2a$

Hence, length of latus rectum $=4a=\frac{14}{\sqrt{17}}$