JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 28

If the circles $x^2+y^2+6x+8y+16=0$ and $x^2+y^2+2\left(3-\sqrt3\right)x+2\left(4-\sqrt6\right)y=k+6\sqrt3+8\sqrt6$, $k>0$, touch internally at the point $P(\alpha,\beta)$, then $\left(\alpha+\sqrt3\right)^2+\left(\beta+\sqrt6\right)^2$ is equal to ______.