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 $
$\sqrt 7 :8$
A focus of an ellipse is at the origin. The directrix is the line $x = 4$ and the eccentricity is $ \frac{1}{2}$ . Then the length of the semi-major axis is
Consider an ellipse with foci at $(5,15)$ and $(21,15)$. If the $X$-axis is a tangent to the ellipse, then the length of its major axis equals
If the normal at any point $P$ on the ellipse cuts the major and minor axes in $G$ and $g$ respectively and $C$ be the centre of the ellipse, then
The equation of the tangent to the ellipse ${x^2} + 16{y^2} = 16$ making an angle of ${60^o}$ with $x$ - axis is
If $PQ$ is a double ordinate of hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ such that $OPQ$ is an equilateral triangle, $O$ being the centre of the hyperbola. Then the eccentricity $e$ of the hyperbola satisfies