The eccentricity of the conic $36x^2 + 144y^2 - 36x - 96y - 119 = 0$ is

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

Let $C$ be the circle of minimum area enclosing the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with eccentricity $e = \frac{1}{2}$ and foci $(\pm 2, 0)$. Let $PQR$ be a variable triangle,whose vertex $P$ is on the circle $C$ and the side $QR$ of length $2$ is parallel to the major axis of $E$ and contains the point of intersection of $E$ with the negative $y$-axis. Then the maximum area of the triangle $PQR$ is:

Let $S$ and $S'$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\Delta S'BS$ is a right-angled triangle with the right angle at $B$ and $\text{Area}(\Delta S'BS) = 8 \text{ sq. units}$,then the length of the latus rectum of the ellipse is

The extremities of the latera recta of the ellipses $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ $(a > b)$ having a given major axis $2a$ lie on:

The eccentricity of the ellipse $9x^2 + 5y^2 - 30y = 0$ is ....