If the points of intersection of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$ and the circle $x^{2}+y^{2}=4b$ (where $b > 4$) lie on the curve $y^{2}=3x^{2}$,then $b$ is equal to:

The length of the chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$,whose mid-point is $(1, \frac{2}{5})$,is equal to:

The locus of the point $P(x, y)$ satisfying the relation $\sqrt{(x - 3)^2 + (y - 1)^2} + \sqrt{(x + 3)^2 + (y - 1)^2} = 6$ is

For an ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ with vertices $A$ and $A'$,a tangent drawn at the point $P$ in the first quadrant meets the $y$-axis at $Q$,and the chord $A'P$ meets the $y$-axis at $M$. If $O$ is the origin,then $OQ^2 - MQ^2$ is equal to:

The position of the point $(4, -3)$ with respect to the ellipse $2x^2 + 5y^2 = 20$ 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: