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

Let the foci of the ellipse $\frac{x^{2}}{9}+y^{2}=1$ subtend a right angle at a point $P$. Then, the locus of $P$ is

If the length of the latus rectum of an ellipse is $4 \ units$ and the distance between a focus and its nearest vertex on the major axis is $\frac{3}{2} \ units$,then its eccentricity is?

The equation of the ellipse whose focus is $(6, 7)$,directrix is $x + y + 2 = 0$,and eccentricity $e = 1/\sqrt{3}$ is:

Let the line $2x + 3y - k = 0, k > 0$,intersect the $x$-axis and $y$-axis at the points $A$ and $B$,respectively. If the equation of the circle having the line segment $AB$ as a diameter is $x^2 + y^2 - 3x - 2y = 0$ and the length of the latus rectum of the ellipse $x^2 + 9y^2 = k^2$ is $\frac{m}{n}$,where $m$ and $n$ are coprime,then $2m + n$ is equal to

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(0, \pm \sqrt{5})$,ends of minor axis $(\pm 1, 0)$.