An ellipse is inscribed in a circle and a point is inside a circle is choosen at random. If the probability that this point lies outside the ellipse is $\frac {2}{3}$ then eccentricity of ellipse is $\frac{{a\sqrt b }}{c}$ . Where $gcd( a, c) = 1$ and $b$ is square free integer ($b$ is not divisible by square of any integer except $1$ ) then $a · b · c$ is

The length of the latus rectum of the ellipse $\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{49}} = 1$

The eccentricity of ellipse $(x-3)^2 + (y -4)^2 = \frac{y^2}{9} +16 ,$ is -

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points $(4,-1)$ and $(-2, 2)$ is

If $A = [(x,\,y):{x^2} + {y^2} = 25]$ and $B = [(x,\,y):{x^2} + 9{y^2} = 144]$, then $A \cap B$ contains

An ellipse having foci at $(3, 3) $ and $(- 4, 4)$  and passing through the origin has eccentricity equal to