Circle: (x−2)2+(y−3)2=16, center O = (2, 3), radius r=4.
For tangents from external point P touching at A and B with ∠AOB=π/3:
In quadrilateral OAPB: ∠APB=π−π/3=2π/3, so ∠OPA=π/3.
In right triangle OAP: sin(π/3)=OP4.
OP=38=383.
Locus: (x−2)2+(y−3)2=364.
3(x2+y2)−12x−18y−25=0.