QJEEM24Ma3162: JEE Main 2024 Mathematics - Class 11 JEEM24Ma3162 Solution: Let the line pass through the point of the intersection (in the …

Let the line $\mathrm{L}: \sqrt{2} x+y=\alpha$ pass through the point of the intersection $\mathrm{P}$ (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola $x^2=2 y$ . Let the line $\mathrm{L}$ touch two circles $\mathrm{C}_1$ and $\mathrm{C}_2$ of equal radius $2 \sqrt{3}$ . If the centres $Q_1$ and $Q_2$ of the circles $C_1$ and $C_2$ lie on the $y$ -axis, then the square of the area of the triangle $\mathrm{PQ}_1 \mathrm{Q}_2$ is equal to ___________.