If $C$ is the centre of the ellipse $9x^2 + 16y^2$ = $144$ and $S$ is one focus. The ratio of $CS$ to major axis, is
$\sqrt 7 :16$
$\sqrt 7 :4$
$\sqrt 5 :\sqrt 7 $
$\sqrt 7 :8$
If the length of the major axis of an ellipse is three times the length of its minor axis, then its eccentricity is
For some $\theta \in\left(0, \frac{\pi}{2}\right),$ if the eccentricity of the hyperbola, $x^{2}-y^{2} \sec ^{2} \theta=10$ is $\sqrt{5}$ times the eccentricity of the ellipse, $x^{2} \sec ^{2} \theta+y^{2}=5,$ then the length of the latus rectum of the ellipse is
An ellipse having foci at $(3, 1)$ and $(1, 1) $ passes through the point $(1, 3),$ then its eccentricity is
An ellipse and a hyperbola have the same centre origin, the same foci and the minor-axis of the one is the same as the conjugate axis of the other. If $ e_1, e_2 $ be their eccentricities respectively, then $e_1^{ - 2} + e_2^{ - 2}$ equals
The equation of the ellipse whose one of the vertices is $(0,7)$ and the corresponding directrix is $y = 12$, is