Question

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

Answer 1

The latus rectum of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is $2\times \frac{16}{5}=\frac{32}{5}$.

Again the double ordinate passing through focus of the parabola $y^2=4ax$ is nothing but the latus rectum and length of it $=4a$.

According to the problem $4a=\frac{32}{5}\Rightarrow a=\frac{8}{5}$.