Mathematics Question from JEE Main 2023 · 31 January, Shift 1

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

Let A and B be the centers of circles $C_1$ and $C_2$ respectively, and M and N be respectively the feet of perpendiculars drawn from A and B on the x-axis. Then the area of the trapezium AMNB is: