Find the equation of the ellipse $(a > b)$ whose distance between the foci is $8$ and the distance between the directrices is $18$.

An ellipse,with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length $4$,passes through which of the following points?

If the normal at one end of a latus rectum of the ellipse $\frac{x^2}{32}+\frac{y^2}{b^2}=1$ passes through one end of the minor axis,then $\frac{e^4}{1-e^2}=$ (Here $e$ is the eccentricity of the ellipse)

If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

The equation of the ellipse having a vertex at $(6,1)$,a focus at $(4,1)$ and the eccentricity $e = \frac{3}{5}$ is

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ be an ellipse with foci $F_1$ and $F_2$. Let $AO$ be its semi-minor axis,where $O$ is the centre of the ellipse. The lines $AF_1$ and $AF_2$,when extended,cut the ellipse again at points $B$ and $C$ respectively. Suppose that the $\triangle ABC$ is equilateral. Then,the eccentricity of the ellipse is