If the distance between a focus and the corresponding directrix of an ellipse is $8$ and the eccentricity is $1/2$,then the length of the minor axis is

The equation of the locus of a point $(2 \cos \theta-3, 3 \sin \theta-4)$ is

The locus of a point such that the sum of its distances from the points $(0, 2)$ and $(0, -2)$ is $6$ is:

Find the eccentricity of an ellipse,if the length of its latus rectum is $4$ units and the distance between its vertex and the nearest focus is $3/2$ units.

Let $E$ be the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$. For any three distinct points $P, Q$ and $Q^{\prime}$ on $E$,let $M(P, Q)$ be the mid-point of the line segment joining $P$ and $Q$,and $M(P, Q^{\prime})$ be the mid-point of the line segment joining $P$ and $Q^{\prime}$. Then the maximum possible value of the distance between $M(P, Q)$ and $M(P, Q^{\prime})$,as $P, Q$ and $Q^{\prime}$ vary on $E$,is:

Tangents are drawn from points on the circle $x^2 + y^2 = 49$ to the ellipse $\frac{x^2}{25} + \frac{y^2}{24} = 1$. The angle between the tangents is: