Question

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

Answer 1

$\frac{x^2}{25}+\frac{y^2}{16}=1$

$\Rightarrow$ length of lalatus rectum $=\frac{2b^2}{a}$

$=2\times 16$

$=32.$

Hence, the answer is $32.$