The equations of the tangents of the ellipse $9{x^2} + 16{y^2} = 144$ which passes through the point $(2, 3)$ is

The latus rectum of an ellipse is $10$ and the minor axis is equal to the distance between the foci. The equation of the ellipse is

A chord $PQ$ of the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ subtends right angle at its  centre. The locus of the point of intersection of tangents drawn at $P$ and $Q$ is-

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(±3,\,0)$ ends of minor axis $(0,\,±2)$

Let the tangents at the points $P$ and $Q$ on the ellipse $\frac{x^{2}}{2}+\frac{y^{2}}{4}=1$ meet at the point $R(\sqrt{2}, 2 \sqrt{2}-2)$. If $S$ is the focus of the ellipse on its negative major axis, then $SP ^{2}+ SQ ^{2}$ is equal to.

The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1$, is .............. $\mathrm{sq. \,units}$