The eccentricity of the ellipse $25x^2 + 16y^2 = 100$ is

If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

If $x^{2}+9 y^{2}-4 x+3=0$,where $x, y \in R$,then $x$ and $y$ respectively lie in the intervals:

The length of the chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{2}=1$,whose mid-point is $\left(1, \frac{1}{2}\right)$,is:

Let $P \left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), Q, R$ and $S$ be four points on the ellipse $9x^2 + 4y^2 = 36$. Let $PQ$ and $RS$ be mutually perpendicular chords passing through the origin. If $\frac{1}{(PQ)^2} + \frac{1}{(RS)^2} = \frac{p}{q}$,where $p$ and $q$ are coprime,then $p+q$ is equal to $.........$.

If the distance between the foci of an ellipse is half the length of its latus rectum,then the eccentricity of the ellipse is