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

Let each of the two ellipses $E_1: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, (a > b)$ and $E_2: \frac{x^2}{A^2} + \frac{y^2}{B^2} = 1, (A < B)$ have eccentricity $\frac{4}{5}$. Let the lengths of the latus recta of $E_1$ and $E_2$ be $\ell_1$ and $\ell_2$, respectively, such that $2\ell_1^2 = 9\ell_2$. If the distance between the foci of $E_1$ is $8$, then the distance between the foci of $E_2$ is:

An ellipse passes through the point $(-3, 1)$ and its eccentricity is $\sqrt{\frac{2}{5}}$. The equation of the ellipse is

The equation of the ellipse in the standard form whose length of the latus rectum is $4$ and whose distance between the foci is $4 \sqrt{2}$,is

The equations of the tangent and normal at point $(3, -2)$ of the ellipse $4x^2 + 9y^2 = 36$ are:

If the distance between the foci of an ellipse is half the length of its latus rectum,then the eccentricity of the ellipse is