x2+y2−6x−6y+14=0 has C1(3,3) and r1=√9+9−14=2 Required centre say C(h, k). Touches y axis ⇒ radius = |h| Touches given circle externally ⇒C1C2=r1+r2 ⇒√(h−3)2+(k−3)2=|h|+2 ⇒h2−6h+9+k2−6k+9=h2+4+4|h| ⇒k2−10h−6k+14=0 ∴ Locus of centre (h,k) is y2−10x−6y+14=0