If the eccentricity of an ellipse is $\frac{5}{8}$ and the distance between its foci is$10,$ then find latus rectum of the ellipse.

If the length of the line-segment joining the vertex of the parabola $y^2=4ax$ point on the parabola where the line-segment makes an angle $\theta$ to the $\mathbf{x}$ -axis is $\frac{ka\cos \theta }{{\sin }^2\theta }$ then $k$ is 

If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2}$ then find $k$, if the equation of hyperbola is $x^2-y^2=k$.