The sum of focal distances of any point on the ellipse with major and minor axes as $2a$ and $2b$ respectively,is equal to

If the sum of the distances from the foci to the centre $O(0,0)$ of an ellipse is $8 \sqrt{6}$ units and the area of the smallest rectangle in which that ellipse is inscribed is $80$ sq. units,then the equation of such an ellipse is

The eccentricity of an ellipse whose latus rectum is equal to the distance between its two foci is:

The foci of the conic $25x^2 + 16y^2 - 150x = 175$ are

The equation of the ellipse whose vertices are $(\pm 5, 0)$ and foci are $(\pm 4, 0)$ is

Tangent to the ellipse $\frac{x^{2}}{32}+\frac{y^{2}}{18}=1$ having slope $-\frac{3}{4}$ meets the coordinate axes at $A$ and $B$. Find the area of the $\Delta AOB$,where $O$ is the origin.