In an ellipse,if the distance between the foci is $6$ units and the length of its minor axis is $8$ units,then its eccentricity is

If the line $y = 2x + c$ is a tangent to the ellipse $\frac{x^2}{8} + \frac{y^2}{4} = 1$,then $c = $

Find the equation of the ellipse which passes through the points $(-3, 1)$ and $(2, -2)$,whose center lies at $(0, 0)$ and major axis lies along the $X$-axis.

The eccentricity of the ellipse $9x^2 + 25y^2 = 225$ is

Planet $M$ orbits around its sun,$S$,in an elliptical orbit with the sun at one of the foci. When $M$ is closest to $S$,it is $2$ units away. When $M$ is farthest from $S$,it is $18$ units away. Assuming $S$ is at the origin $(0, 0)$ and the other focus lies on the negative $y$-axis,find the equation of the elliptical orbit of planet $M$.

The product of the perpendiculars from the two foci of the ellipse $\frac{x^2}{9} + \frac{y^2}{25} = 1$ on the tangent at any point on the ellipse is: