CAT 2023 Coordinate Geometry — Previous Year Question

Let $\mathrm{C}$ be the circle $x^2+y^2+4x-6y-3=0$ and $\mathrm{L}$ be the locus of the point of intersection of a pair of tangents to $\mathrm{C}$ with the angle between the two tangents equal to $60^{\circ}$. Then, the point at which $L$ touches the line $x=6$ is