If $C$ is the centre of the ellipse $9x^2 + 16y^2 = 144$ and $S$ is one focus,then the ratio of $CS$ to the major axis is:

If a tangent to the ellipse $x^{2}+4y^{2}=4$ meets the tangents at the extremities of its major axis at $B$ and $C$,then the circle with $BC$ as diameter passes through the point:

If $4x + 2y + n = 0$ is a normal to the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$,then $n = $

The equations of the directrices of the ellipse $16x^2 + 25y^2 = 400$ are

Let $E_1: \frac{x^2}{9}+\frac{y^2}{4}=1$ be an ellipse. Ellipses $E_i$ are constructed such that their centres and eccentricities are the same as that of $E_1$,and the length of the minor axis of $E_i$ is the length of the major axis of $E_{i+1}$ $(i \geq 1)$. If $A_i$ is the area of the ellipse $E_i$,then $\frac{5}{\pi}\left(\sum_{i=1}^{\infty} A_i\right)$ is equal to . . . . . . .

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