Question

If latus rectum of ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is double ordiante of parabola $y^2=4ax$ value of a is

• A. $\frac{64}{25}$
• B. $\frac{25}{64}$
• C. $\frac{64}{50}$
• D. $\frac{64}{75}$

Answer 1

Answer: (D)

$e=\sqrt{1-\frac{16}{25}}=\frac{3}{5}$
End points of latus rectum $\left(3,\frac{16}{5}\right)$
put in $y^2=4x\Rightarrow \frac{256}{25}=4a(3)$
$\Rightarrow a=\frac{64}{75}$