If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $90^{\circ}$,then its eccentricity is

If the latus rectum of an ellipse is equal to half of its minor axis,then its eccentricity is

For the ellipse $4x^2 + y^2 - 8x + 2y + 1 = 0$,the focus and the equation of the directrix are respectively

$A$ variable tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ makes intercepts on both the axes. The locus of the midpoint of the portion of the tangent between the coordinate axes is

Let $x = 9$ be a directrix of an ellipse $E$, whose centre is at the origin and eccentricity is $1/3$. Let $P(\alpha, 0), \alpha > 0$, be a focus of $E$ and $AB$ be a chord passing through $P$. Then the locus of the mid point of $AB$ is :

The length of the latus-rectum of the ellipse,whose foci are $(2,5)$ and $(2,-3)$ and eccentricity is $\frac{4}{5}$,is