In an ellipse,its foci and the ends of its major axis are equally spaced. If the length of its semi-minor axis is $2 \sqrt{2}$,then the length of its semi-major axis is

The length of the latus rectum of $9x^2 + 25y^2 - 90x - 150y + 225 = 0$ is

The value of $k$ such that the line $y=2x+k$ touches the ellipse $3x^2+5y^2=15$ is

The equations of the tangents drawn at the ends of the major axis of the ellipse $9x^2 + 5y^2 - 30y = 0$ are:

Let $A$ be a vertex of the ellipse $S \equiv \frac{x^2}{4}+\frac{y^2}{9}-1=0$ and $F$ be a focus of the ellipse $S^{\prime} \equiv \frac{x^2}{9}+\frac{y^2}{4}-1=0$. Let $P$ be a point on the major axis of the ellipse $S^{\prime}=0$,which divides $\overline{OF}$ in the ratio $2:1$ ($O$ is the origin). If the length of the chord of the ellipse $S=0$ through $A$ and $P$ is $\frac{3\sqrt{101}}{k}$,then $k=$

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