Mathematics Tes...

If the distance between directrices is thrice the distance between focii of an ellipse, then its eccentricity is -

Suppose an ellipse and a hyperbola have the same pair of foci on the x- axis with centres at the origin and that they intersect at (2,2). If the eccentricity of the ellipse is 1/2, then the eccentricity of the hyperbola is

A line makes some angle $\theta$, with each of the and axis. If the angle $\beta$ which it makes with axis is such that ${\sin }^2\beta =3{\sin }^2\theta$ then $5{\cos }^2\theta$ equals