If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{4 a^{2}}=1$ and the co-ordinate axis is $kab,$ then $\mathrm{k}$ is equal to ..... .
$1$
$3$
$2$
$7$
If the angle between the lines joining the end points of minor axis of an ellipse with its foci is $\pi\over2$, then the eccentricity of the ellipse is
A wall is inclined to the floor at an angle of $135^{\circ}$. A ladder of length $l$ is resting on the wall. As the ladder slides down, its mid-point traces an arc of an ellipse. Then, the area of the ellipse is
The locus of the foot of perpendicular drawn from the centre of the ellipse ${x^2} + 3{y^2} = 6$ on any tangent to it is
Eccentricity of the conic $16{x^2} + 7{y^2} = 112$ is
Eccentricity of the ellipse whose latus rectum is equal to the distance between two focus points, is