Let a circle C_1 be obtained on rolling the circle x^2+y^2-4 x-6 y+11=0 upwards 4 units on the tangent T to it at the point (3,2). Let C_2 be the…

Let a circle $\displaystyle C_1$ be obtained on rolling the circle $\displaystyle x^2+y^2-4 x-6 y+11=0$ upwards $\displaystyle 4$ units on the tangent T to it at the point $\displaystyle (3,2)$. Let $\displaystyle C_2$ be the image of $\displaystyle C_1$ in T . Let $\displaystyle A$ and $\displaystyle B$ be the centers of circles $\displaystyle C_1$ and $\displaystyle C_2$ respectively, and $\displaystyle M$ and $\displaystyle N$ be respectively the feet of perpendiculars drawn from $\displaystyle A$ and $\displaystyle B$ on the $\displaystyle x$-axis. Then the area of the trapezium AMNB is :