The sum of the focal distances of the point $\left(\frac{4}{\sqrt{5}}, \frac{3}{\sqrt{5}}\right)$ on the ellipse $9x^2+4y^2=36$ is

The area of the region enclosed by the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is . . . . . . square units. (in $\pi$)

The sum of focal radii of the curve $9x^{2} + 25y^{2} = 225$ is

If $6x - 5y - 20 = 0$ is a normal to the ellipse $x^2 + 3y^2 = k$,then $k =$

Let $S_{1}: x^{2}+y^{2}=9$ and $S_{2}:(x-2)^{2}+y^{2}=1$. Then the locus of the center of a variable circle $S$ which touches $S_{1}$ internally and $S_{2}$ externally always passes through the points :

The line $lx + my - n = 0$ will be tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,if