The eccentricity of the ellipse $\left( \frac{x - 3}{y} \right)^2 + \left( 1 - \frac{4}{y} \right)^2 = \frac{1}{9}$ is

If the normal at one end of the latus rectum of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ passes through one end of the minor axis,then:

When does the line $x \cos \alpha + y \sin \alpha = p$ touch the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$?

If the radius of the largest circle with centre $(2,0)$ inscribed in the ellipse $x^2+4y^2=36$ is $r$,then $12r^2$ is equal to

If $S$ and $S^{\prime}$ are the foci of an ellipse $\frac{x^2}{169}+\frac{y^2}{144}=1$ and the point $B$ lying on the positive $Y$-axis is one end of its minor axis,then the incenter of the triangle $SBS^{\prime}$ is

If the angle between the lines joining the end points of the minor axis of an ellipse with its foci is $\frac{\pi}{2}$,then the eccentricity of the ellipse is