If the centre, one of the foci and semi-major axis of an ellipse be $(0, 0), (0, 3)$ and $5$ then its equation is
$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = 1$
$\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1$
$\frac{{{x^2}}}{9} + \frac{{{y^2}}}{{25}} = 1$
None of these
The point $(4, -3)$ with respect to the ellipse $4{x^2} + 5{y^2} = 1$
If the ellipse $\frac{ x ^{2}}{ a ^{2}}+\frac{ y ^{2}}{ b ^{2}}=1$ meets the line $\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1$ on the $y$-axis, then the eccentricity of the ellipse is
An ellipse is drawn with major and minor axes of lengths $10 $ and $8$ respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is
Tangent is drawn to ellipse $\frac{{{x^2}}}{{27}} + {y^2} = 1$ at $(3\sqrt 3 \cos \theta ,\;\sin \theta )$ where $\theta \in (0,\;\pi /2)$. Then the value of $\theta $ such that sum of intercepts on axes made by this tangent is minimum, is