In an ellipse $9x^2 + 5y^2 = 45$,the distance between the foci is

If the curves $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $\frac{x^2}{25}+\frac{y^2}{16}=1$ cut each other orthogonally, then $a^2-b^2$ equals to

If the chords of contact of tangents drawn from two points $(x_1, y_1)$ and $(x_2, y_2)$ to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are at right angles,then $\frac{x_1 x_2}{y_1 y_2} = \dots$

If $P$ is any point on the ellipse $16x^2 + 25y^2 = 400$ with foci $S$ and $S'$, and the area of $\Delta PSS'$ is $9 \text{ square units}$, then the abscissa of point $P$ is:

If $y = mx + c$ is a tangent to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,then the value of $c$ is ...

If the midpoint of a chord of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ is $(\sqrt{2}, 4/3)$,and the length of the chord is $\frac{2 \sqrt{\alpha}}{3}$,then $\alpha$ is :