Question

The equation of directrix and latus rectum of a parabola are $3x-4y+27=0$ and $3x-4y+2=0$. Then the length of latus rectum is

• A. $5$
• B. $10$
• C. $15$
• D. $20$

Answer 1

Answer: (B)

$10$

$d=\left|\frac{C_1-C_2}{\sqrt{a^2+b^2}}\right|$
where $d$ is the distance between lines whose equations are $ax+by+C_1=0$ & $ax+by+C_2=0$
$d=\left|\frac{27-2}{\sqrt{4^2+3^2}}\right|$
$=5$
$d=5$
If the distance between vertex and latus rectum$=$distance of vertex from directrix$=a$

then $d=2a=5$
$\Rightarrow$ Length of latus rectum$=4a=10$