An ellipse is inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is $2/3 $ then the eccentricity of the ellipse is :

Length of common chord of the ellipse ${\frac{{\left( {x – 2} \right)}}{9}^2} + {\frac{{\left( {y + 2} \right)}}{4}^2} = 1$ and the circle ${x^2} + {y^2} – 4x + 2y + 4 = 0$

Locus of the foot of the perpendicular drawn from the centre upon any tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, is

Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E: \frac{x^2}{6}+\frac{y^2}{3}=1$ and the parabola $P: y^2=12 x$. Suppose that the tangent $T_1$ touches $P$ and $E$ at the point $A_1$ and $A_2$, respectively and the tangent $T_2$ touches $P$ and $E$ at the points $A_4$ and $A_3$, respectively. Then which of the following statements is(are) true?

($A$) The area of the quadrilateral $A_1 A _2  A _3 A _4$ is $35$ square units

($B$) The area of the quadrilateral $A_1 A_2 A_3 A_4$ is $36$ square units

($C$) The tangents $T_1$ and $T_2$ meet the $x$-axis at the point $(-3,0)$

($D$) The tangents $T_1$ and $T_2$ meet the $x$-axis at the point $(-6,0)$

The eccentricity of an ellipse whose length of latus rectum is equal to distance between its foci, is