Consider an ellipse with foci at $(5,15)$ and $(21,15)$. If the $X$-axis is a tangent to the ellipse, then the length of its major axis equals

The area (in sq, 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 :

P is any point on the ellipse $9{x^2} + 36{y^2} = 324$, whose foci are $S$ and $S’$. Then $SP + S'P$ equals

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $\frac{x^{2}}{36}+\frac{y^2} {16}=1$

The equation of the normal at the point $(2, 3)$ on the ellipse $9{x^2} + 16{y^2} = 180$, is

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