The locus of the centre of a circle which touches externally the circle and also touches the y-axis is given by the equation
Let the centre of the circle be . Since the circle touches the axis of . Therefore, radius.
The radius of the circle 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
Hence, the locus of ( is .