Tangents at extremities of latus rectum of ellipse $3x^2 + 4y^2 = 12$ form a rhombus of area (in $sq.\ units$) -

If a number of ellipse be described having the same major axis $2a$  but a variable minor axis then the tangents at the ends of their latera recta pass through fixed points which can be

In an ellipse, the distance between its foci is $6$ and minor axis is $8$. Then its eccentricity is

How many real tangents can be drawn to the ellipse $5x^2 + 9y^2 = 32$ from the point $(2,3)$

If the tangent at a point on the ellipse $\frac{{{x^2}}}{{27}} + \frac{{{y^2}}}{3} = 1$ meets the coordinate axes at $A$ and $B,$  and  $O$  is the origin, then the minimum area (in sq. units) of the triangle $OAB$  is

If the lines $x -2y = 12$ is tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ at the point $\left( {3,\frac{-9}{2}} \right)$, then the length of the latus rectum of the ellipse is