In an ellipse,the minor axis is $8$ and the eccentricity is $\frac{\sqrt{5}}{3}$. Then the major axis is:

Find the equation of the ellipse whose center is at $(2, -3)$,focus is at $(3, -3)$,and one vertex is at $(4, -3)$.

If the distance between the two foci of an ellipse is equal to its minor axis,then the eccentricity of the ellipse is:

$A$ point $(4, -1)$ lies on an ellipse whose axes are parallel to the coordinate axes. If the line $x + 4y - 10 = 0$ is tangent to the ellipse at this point,find its equation $(a > b)$.

The tangent to the ellipse $9x^2 + 16y^2 = 288$ making equal intercepts on the coordinate axes intersects the $X$-axis and the $Y$-axis at points $A$ and $B$ respectively. Then,the area of $\triangle OAB$ (where $O$ is the origin) is:

If $3x + 4y = 12\sqrt{2}$ is a tangent to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{9} = 1$ for some $a \in R$,then the distance between the foci of the ellipse is: