The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1$, is .............. $\mathrm{sq. \,units}$

An ellipse having foci at $(3, 1)$ and $(1, 1) $ passes through the point $(1, 3),$ then its eccentricity is

Let $A,B$ and $C$ are three points on ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$where line joing $A \,\,\&\,\, C$ is parallel to the $x-$axis and $B$ is end point of minor axis whose ordinate is positive then maximum area of $\Delta ABC,$ is-

Find the equation for the ellipse that satisfies the given conditions: $b=3,\,\, c=4,$ centre at the origin; foci on the $x$ axis.

The angle between the pair of tangents drawn to the ellipse $3{x^2} + 2{y^2} = 5$ from the point $(1, 2)$, is

Let $A = \left\{ {\left( {x,y} \right):\,y = mx + 1} \right\}$ 

      $B = \left\{ {\left( {x,y} \right):\,\,{x^2} + 4{y^2} = 1} \right\}$ 

$C = \left\{ {\left( {\alpha ,\beta } \right):\,\left( {\alpha ,\beta } \right) \in A\,\,and\,\,\left( {\alpha ,\beta } \right) \in B\,\,and\,\alpha \, > 0} \right\}$ . 

If set $C$ is singleton set then sum of all possible values of $m$ is