The angle between the pair of tangents drawn to the ellipse $3{x^2} + 2{y^2} = 5$ from the point $(1, 2)$, is
${\tan ^{ - 1}}\left( {\frac{{12}}{5}} \right)$
${\tan ^{ - 1}}(6\sqrt 5 )$
${\tan ^{ - 1}}\left( {\frac{{12}}{{\sqrt 5 }}} \right)$
${\tan ^{ - 1}}(12\sqrt 5 )$
Area of the quadrilaterals formed by drawing tangents at the ends of latus recta of $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{1} = 1$ is
In an ellipse, its foci and ends of its major axis are equally spaced. If the length of its semi-minor axis is $2 \sqrt{2}$, then the length of its semi-major axis is
The ellipse $E_1: \frac{x^2}{9}+\frac{y^2}{4}=1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes.
Another ellipse $E _2$ passing through the point $(0,4)$ circumscribes the rectangle $R$.. The eccentricity of the ellipse $E _2$ is
Let $P(a\sec \theta ,\;b\tan \theta )$ and $Q(a\sec \varphi ,\;b\tan \varphi )$, where $\theta + \phi = \frac{\pi }{2}$, be two points on the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$. If $(h, k)$ is the point of intersection of the normals at $P$ and $Q$, then $k$ is equal to
The eccentricity of ellipse $(x-3)^2 + (y -4)^2 = \frac{y^2}{9} +16 ,$ is -