The locus of centre of a circle which touches externally the circle x2+y2−6x−6y+14=0  and also touch the y  -axis is given by the equation

Let centre of the circle be (h,k) ∵  circle touch y -axis∴  radius =|h| Equation of circle is (x−h)2+(y−k)2=h2 ………………(i)Given circle (i) touches externally the circlex2+y2−6x−6y+14=0 ∴  Distance between centres = sum of radii(h−3)2+(k−3)2=|h|+2 ⇒(h−3)2+(k−3)2=h2+4+4|h| ⇒k2−6h−4|h|−6k+14=0 Here h  always +ve∴k2−10h−6k+14=0 ∴  Locus of centre of circle isy2−10x−6y+14=0