let (a,b) be the center.
the radius is sqrt( [a+2]^2 + [b-3]^2 )
same with. its distance from (a,b) to the line x = 6. which is |a-6|
comparing the 2 radii,
[a+2]^2 + [b-3]^2 = (a-6)^2
a^2 + 4a + 4 + b^2 - 6b + 9 = a^2 - 12a + 36
16a + b^2 - 23 - 6b = 0
a = x, b = y.
16x + y^2 - 23 - 6y = 0.
therefore, the locus is y^2 - 6y - 23 + 16x = 0.
