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

Let the centre of the circle be (h, k). Since the circle touches the axis of y. Therefore, radius.= h.The radius of the circle x2+y2−6x−6y+14=0 is 2 and it has its centre at (3, 3). It is given that the two circles touch each other externally∴   Distance between the centres = Sum of the radii⇒ (h−3)2+(k−3)2=h+2⇒ k2−10h-6k+14=0Hence, the locus of (h,k is y2−10x−6y+14=0.