An ellipse has $OB$ as semi-minor axis,$F$ and $F'$ as its foci,and the angle $\angle FBF'$ is a right angle. Then the eccentricity of the ellipse is

For the ellipse given by $\frac{(x-3)^2}{25}+\frac{(y-2)^2}{16}=1$,match the equations of the lines given in List-$I$ with those on the List-$II$.

List-$I$	List-$II$
$(i)$ The equation of the major axis	$(p)$ $3x = 34$
$(ii)$ The equation of a directrix	$(q)$ $y = 2$
$(iii)$ The equation of a latus rectum	$(r)$ $x + y = 9$
	$(s)$ $x = 6$
	$(t)$ $x = 3$
	$(u)$ $3y = 34$

The distance of the point $\theta$ on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ from a focus is

The point $(1,3)$ with respect to the ellipse $4x^2+9y^2-16x-54y+61=0$ lies

Let $E_{1}: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a > b$. Let $E_{2}$ be another ellipse such that it touches the end points of the major axis of $E_{1}$ and the foci of $E_{2}$ are the end points of the minor axis of $E_{1}$. If $E_{1}$ and $E_{2}$ have the same eccentricity $e$,then the value of $e$ is:

The eccentricity of the ellipse $x^2+4 y^2+2 x+16 y+13=0$ is