If the angle between the lines joining the end points of the minor axis of an ellipse with its foci is $\frac{\pi}{2}$,then the eccentricity of the ellipse is

Consider ellipses $E_{k}: kx^{2} + k^{2}y^{2} = 1$,for $k = 1, 2, \ldots, 20$. Let $C_{k}$ be the circle which touches the four chords joining the end points (one on the minor axis and another on the major axis) of the ellipse $E_{k}$. If $r_{k}$ is the radius of the circle $C_{k}$,then the value of $\sum_{k=1}^{20} \frac{1}{r_{k}^{2}}$ is $.......$.

If a tangent with slope $-4/3$ to the ellipse $\frac{x^2}{18} + \frac{y^2}{32} = 1$ intersects the major axis and minor axis at $A$ and $B$ respectively,then the area of $\Delta OAB$ is .......... square units.

The equation of the ellipse whose one focus is at $(4, 0)$ and whose eccentricity is $4/5$,is

Number of points on the ellipse $\frac{x^2}{50} + \frac{y^2}{20} = 1$ from which a pair of perpendicular tangents are drawn to the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is:

If the line $y = 2x + c$ is a tangent to the ellipse $\frac{x^2}{8} + \frac{y^2}{4} = 1$,then $c = $