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  4. If latus rectum of ellipse (x2/25)+(y2/16)=1 is double ordiante of parabola y2=4 a x value of a is

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

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Solution:

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