If tangents are drawn from the point ($2 + 13cos\theta , 3 + 13sin\theta $) to the ellipse $\frac{(x-2)^2}{25} + \frac{(y-3)^2}{144} = 1,$ then angle between them, is

Let the line $y=m x$ and the ellipse $2 x^{2}+y^{2}=1$ intersect at a ponit $\mathrm{P}$ in the first quadrant. If the normal to this ellipse at $P$ meets the co-ordinate axes at $\left(-\frac{1}{3 \sqrt{2}}, 0\right)$ and $(0, \beta),$ then $\beta$ is equal to

If any tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ cuts off intercepts of length $h$ and $k$ on the axes, then $\frac{{{a^2}}}{{{h^2}}} + \frac{{{b^2}}}{{{k^2}}} = $

A tangent to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ intersect the co-ordinate axes at $A$ and $B,$ then locus of circumcentre of triangle $AOB$ (where $O$ is origin) is

The eccentricity of the ellipse $4{x^2} + 9{y^2} + 8x + 36y + 4 = 0$ is