If the area of the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{\lambda^{2}}=1$ is $20 \pi$ sq units,then $\lambda$ is

If $\alpha x+\beta y=109$ is the equation of the chord of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$,whose midpoint is $\left(\frac{5}{2}, \frac{1}{2}\right)$,then $\alpha+\beta$ is equal to

If $S$ and $S^{\prime}$ are the foci of an ellipse,$B$ is one end of the minor axis and $\angle SBS^{\prime} = 90^{\circ}$,then the eccentricity of that ellipse is

The equation of an ellipse,whose vertices are $(2, -2)$ and $(2, 4)$ and eccentricity is $\frac{1}{3}$,is

Let $L$ be the distance between two parallel normals of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ where $a > b$. Then the maximum value of $L$ is:

The area (in square units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\frac{x^2}{9} + \frac{y^2}{5} = 1$ is: