The eccentricity of the ellipse $25{x^2} + 16{y^2} - 150x - 175 = 0$ is

How many real tangents can be drawn to the ellipse $5x^2 + 9y^2 = 32$ from the point $(2,3)$

In an ellipse, the distance between its foci is $6$ and minor axis is $8$. Then its eccentricity is

If a number of ellipse be described having the same major axis $2a$  but a variable minor axis then the tangents at the ends of their latera recta pass through fixed points which can be

For an ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ with vertices $A$  and $ A', $ tangent drawn at the point $P$  in the first quadrant meets the $y-$axis in $Q $ and the chord $ A'P$ meets the $y-$axis in $M.$  If $ 'O' $ is the origin then $OQ^2 - MQ^2$  equals to

Area (in sq. units) of the region outside $\frac{|\mathrm{x}|}{2}+\frac{|\mathrm{y}|}{3}=1$ and inside the ellipse $\frac{\mathrm{x}^{2}}{4}+\frac{\mathrm{y}^{2}}{9}=1$ is