If $C$ is the centre of the ellipse $9x^2 + 16y^2$ = $144$ and $S$ is one focus. The ratio of $CS$ to major axis, is 

An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ and the parabola $x^2=4(y+b)$ are such that the two foci of the ellipse and the end points of the latusrectum of parabola are the vertices of a square. The eccentricity of the ellipse is

For the ellipse $3{x^2} + 4{y^2} = 12$, the length of latus rectum is

The equation of the normal to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ at the point $(a\cos \theta ,\;b\sin \theta )$ is

The minimum area of a triangle formed by any tangent to the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{81}} = 1$ and the coordinate axes is 

If the angle between the lines joining the end points of minor axis of an ellipse with its foci is $\pi\over2$, then the eccentricity of the ellipse is