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

If the centre,one of the foci,and the semi-major axis of an ellipse are $(0, 0)$,$(0, 3)$,and $5$ respectively,then its equation is:

$A$ man running round a race-course notes that the sum of the distances of two flag-posts from him is always $10 \ m$ and the distance between the flag-posts is $8 \ m$. The area of the path he encloses in square metres is (in $\pi$)

One of the foci of an ellipse is $(2,-3)$ and its corresponding directrix is $2x+y=5$. If the eccentricity of the ellipse is $\frac{\sqrt{5}}{3}$,then the coordinates of the other focus are

The minimum distance between two points $P$ and $Q$ on the ellipse $\frac{x^2}{25} + \frac{y^2}{4} = 1$,if the difference between the eccentric angles of $P$ and $Q$ is $\frac{3\pi}{2}$,is

The position of the point $(1, 3)$ with respect to the ellipse $4x^2 + 9y^2 - 16x - 54y + 61 = 0$ is: