Let $A_1$ be the area of the given ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Let $A_2$ be the area of the region bounded by the curve which is the locus of mid-point of the line segment joining the focus of the ellipse and a point $P$ on the given ellipse, then $A_1: A_2=$

The angle between the tangents drawn from a point $(-3,2)$ to the ellipse $4 x^2+9 y^2-36=0$ is

The equation of a chord $A B$ of an ellipse $2 x^2+y^2=1$ is $x-y+1=0$. If $O$ is the origin, then $\sqrt{A O B}=$

The square of the slope of a common tangent drawn to the circle $4 x^2+4 y^2=25$ and the ellipse $4 x^2+9 y^2=36$ is