If the point of contact of the circles $x^2+y^2-6 x-4 y+9=0$ and $x^2+y^2+2 x+2 y-7=0$ is $(\alpha, \beta)$, then $7 \beta=$

If the circles $x^2+y^2-2 \lambda x-2 y-7=0$ and $3\left(x^2+y^2\right)-8 x+29 y=0$ are orthogonal, then $\lambda=$

If the perpendicular distance from the focus of a parabola $y^2=4 a x$ to its directrix is $\frac{3}{2}$, then the equation of the normal drawn at $(4 a,-4 a)$ is

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 $A_1: A_2=$