What is the locus of the point of intersection of perpendicular tangents to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$?

If $CP$ and $CD$ are a pair of semi-conjugate diameters of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$,then $CP^{2}+CD^{2}=$

The equation $\frac{x^2}{10-a} + \frac{y^2}{4-a} = 1$ represents an ellipse when:

If the eccentricity of an ellipse is $1/\sqrt{2}$,then its latus rectum is equal to its

If the line joining the points $A(\alpha)$ and $B(\beta)$ on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ is a focal chord,then one possible value of $\cot \frac{\alpha}{2} \cdot \cot \frac{\beta}{2}$ is

In an ellipse,the minor axis is $8$ and the eccentricity is $\frac{\sqrt{5}}{3}$. Then the major axis is: