If $A$ and $B$ are two fixed points and $P$ is a variable point such that $PA + PB = 4$,then the locus of $P$ is a/an

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ and having its center at $(0, 3)$ is:

$A$ tangent is drawn to the ellipse $\frac{x^2}{27} + y^2 = 1$ at the point $(3\sqrt{3} \cos \theta, \sin \theta)$ where $\theta \in (0, \pi/2)$. The value of $\theta$ for which the sum of the intercepts on the axes made by this tangent is minimum,is:

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

The lengths of the major and minor axes of an ellipse are $10$ and $8$ respectively,and its major axis lies along the $y$-axis. The equation of the ellipse,with its center at the origin,is:

If the length of the major axis of an ellipse is three times the length of its minor axis,then its eccentricity is