The equation $\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4$,where $-2 < x < 2$,represents a

An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ $(a>b)$ is inscribed in a rectangle of dimensions $2a$ and $2b$ respectively. If the angle between the diagonals of the rectangle is $\tan^{-1}(4\sqrt{3})$,then the eccentricity of that ellipse is

One of the foci of an ellipse is $(2,-3)$ and its corresponding directrix is $2x+y=5$. If the eccentricity of the ellipse is $\frac{\sqrt{5}}{3}$,then the coordinates of the other focus are

$A$ rectangle of maximum area is inscribed in an ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$. Then its dimensions are:

What is the locus of the point of intersection of perpendicular tangents to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$?

In an ellipse,let $B$ be one end of the minor axis,$F$ and $F'$ be the foci,and $\angle FBF' = 90^{\circ}$. Then the eccentricity of the ellipse is: