The eccentric angles of the extremities of latus recta of the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ are given by

A circle has the same centre as an ellipse and passes through the foci $F_1 \& F_2$  of the ellipse, such that the two curves intersect in $4$  points. Let $'P'$  be any one of their point of intersection. If the major axis of the ellipse is $17 $ and  the area of the triangle $PF_1F_2$ is $30$, then the distance between the foci is :

The co-ordinates of the foci of the ellipse $3{x^2} + 4{y^2} - 12x - 8y + 4 = 0$ are

Let $A,B$ and $C$ are three points on ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$where line joing $A \,\,\&\,\, C$ is parallel to the $x-$axis and $B$ is end point of minor axis whose ordinate is positive then maximum area of $\Delta ABC,$ is-

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis $16$ foci $(0,\,±6)$

If the angle between the lines joining the end points of minor axis of an ellipse with its foci is $\pi\over2$, then the eccentricity of the ellipse is