The locus of the point of intersection of the perpendicular tangents to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ is

Find the coordinates of the foci,the vertices,the length of the major axis,the minor axis,the eccentricity,and the length of the latus rectum of the ellipse $16x^{2} + y^{2} = 16$.

An ellipse has its center at $(1, -2)$, one focus at $(3, -2)$, and one vertex at $(5, -2)$. Then the length of its latus rectum is :

If $P$ is a point on $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ with foci $S$ and $S^{\prime}$,then the maximum area of $\triangle S P S^{\prime}$ is

An ellipse is described by using an endless string which is passed over two pins. If the axes are $6 \ cm$ and $4 \ cm$,the necessary length of the string and the distance between the pins respectively in $cm$,are

The locus of a point such that the sum of its distances from the points $(0, 2)$ and $(0, -2)$ is $6$ is: