Find the locus of a point from which the lengths of the tangents to the circles $x^2+y^2+4x+3=0$ and $x^2+y^2-6x+5=0$ are in the ratio $2:3$.
My Attempt:
Given circles are: $$x^2+y^2+4x+3=0$$ and, $$x^2+y^2-6x+5=0$$. Let, $P(x_1,y_1)$ be a point on the locus, and $T_1$ and $T_2$ be the lengths of tangents.
According to question: $T_1:T_2=2:3$ $\frac {T_1}{T_2}=\frac {2}{3}$ $3T_1=2T_2$.
Please help me to continue from here.