Find the equation of the ellipse whose latus rectum is $10$ and the length of the minor axis is equal to the distance between the foci.

The foci of the ellipse $2x^2 + 3y^2 - 4x - 12y + 13 = 0$ are

Consider an ellipse,whose centre is at the origin and its major axis is along the $x-$ axis. If its eccentricity is $\frac{3}{5}$ and the distance between its foci is $6$,then the area (in sq. units) of the quadrilateral inscribed in the ellipse,with the vertices as the vertices of the ellipse,is

The locus of the mid-points of the chords of an ellipse $x^{2}+4y^{2}=4$ that are drawn from the positive end of the minor axis is

The locus of the point of intersection of two perpendicular tangents to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ is:

If $P(\theta)$ and $Q\left(\frac{\pi}{2}+\theta\right)$ are two points on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the locus of the midpoint of $PQ$ is $\frac{x^2}{\alpha^2}+\frac{y^2}{\beta^2}=1$,then $\frac{a+b}{\alpha+\beta}=$