CAT 2023 Slot 1 QA Question 18: Let C be the circle $x^2 + y^2 + 4x - 6y - 3 = 0$ 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 $60^\circ$. Then, the poin

Question

Let C be the circle $x^2 + y^2 + 4x - 6y - 3 = 0$ 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 $60^\circ$. Then, the poin

Accepted Answer

Rewrite the given circle by completing squares.

$x^2 + y^2 + 4x - 6y - 3 = 0$
$(x+2)^2 + (y-3)^2 = 16$

So the centre is $O(-2,3)$ and the radius is $r=4$.

Let P be the point from which the two tangents are drawn. If the angle between tangents is $60^\circ$, then $OP$ bisects this angle. In the ri

Let C be the circle x2+y2+4x−6y−3=0x^2 + y^2 + 4x - 6y - 3 = 0x2+y2+4x−6y−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 60∘60^\circ60∘. Then, the point at which L touches the line x=6x = 6x=6 is

Let C be the circle $x^2 + y^2 + 4x - 6y - 3 = 0$ 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 $60^\circ$ . Then, the point at which L touches the line $x = 6$ is