The eccentricity of the ellipse $4{x^2} + 9{y^2} + 8x + 36y + 4 = 0$ is
$\frac{5}{6}$
$\frac{3}{5}$
$\frac{{\sqrt 2 }}{3}$
$\frac{{\sqrt 5 }}{3}$
The distance of the point $'\theta '$on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ from a focus is
Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(±3,\,0)$ ends of minor axis $(0,\,±2)$
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
If the normal at the point $P(\theta )$ to the ellipse $\frac{{{x^2}}}{{14}} + \frac{{{y^2}}}{5} = 1$ intersects it again at the point $Q(2\theta )$, then $\cos \theta $ is equal to
The area (in sq, units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1$ is :