Let \mathrm{C} be the circle x^2+y^2+4 x-6 y-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

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CAT 2023 Slot 1 QA · Question 17

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

A.
(6,4)
B.
(6,8)
C.
(6,3)
D.
(6,6)

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