The sum of the focal distances of any point on the conic $\frac{x^2}{25} + \frac{y^2}{16} = 1$ is

The eccentric angle of the point $P(-6, 2)$ on the ellipse $\frac{x^2}{48} + \frac{y^2}{16} = 1$ is: (in $^{\circ}$)

The sides of the rectangle of greatest area that can be inscribed in the ellipse $x^2+4y^2=64$ are :

The equations of two ellipses are $\frac{x^2}{4}+\frac{y^2}{2}=1$ and $\frac{x^2}{36}+\frac{y^2}{b^2}=1$. If the product of their eccentricities is $\frac{\sqrt{2}}{3}$,then the product of the length of the major axis and minor axis of the second ellipse is $\qquad$

The area (in sq. units) of the quadrilateral formed by the tangents drawn at the end points of the latus rectum to the ellipse $S \equiv \frac{x^2}{16}+\frac{y^2}{12}=1$ is

The minimum area of a triangle formed by any tangent to the ellipse $\frac{x^2}{16} + \frac{y^2}{81} = 1$ and the coordinate axes is