The eccentricity of the ellipse $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$ is

Let $F$ and $F'$ be the foci of the ellipse $\frac{x^2}{4}+\frac{y^2}{b^2}=1$ $(b < 2)$ and $B$ is one end of the minor axis. If the area of the triangle $FBF'$ is $\sqrt{3}$ sq. units,then the eccentricity of the ellipse is

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is $90^{\circ}$. The eccentricity of the ellipse is

The equations of the directrices of the ellipse $16x^2 + 25y^2 = 400$ are

The length of the latus rectum of the ellipse $4x^2 + 9y^2 - 8x - 36y + 4 = 0$ is

If tangents are drawn from point $P(3 \sin \theta + 4 \cos \theta, 3 \cos \theta - 4 \sin \theta)$ where $\theta = \frac{\pi}{8}$ to the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$,then the angle between the tangents is: