If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity 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 equations of the directrices of the ellipse $16x^2 + 25y^2 = 400$ are

The equations of the tangents to the ellipse $9x^2 + 16y^2 = 144$ which pass through the point $(2, 3)$ are

The ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and the straight line $y = mx + c$ intersect in real points only if

Let a tangent to the curve $9x^2 + 16y^2 = 144$ intersect the coordinate axes at the points $A$ and $B$. Then,the minimum length of the line segment $AB$ is $.........$