Equation of circle

It is given that theequation of circle C1 is x² + y² + 4x - 2y - 59 = 0, and the centre of circleC2 is (1, 5). If C2 lies inside C1 andthey touch each other internally,
find the equation if C2.


C1: x² + y² + 4x - 2y - 59 = 0
Centre of C1, O1= (-4/2, -(-2)/2) = (-2, 1)
Radius of C1, r1= √[(4/2)² + (-2/2)² - (-59)] = 8

Centre of C2,O2= (1, 5)
Radius of C2 = r2

C2 lies inside C1 and they touch each other internally:
r1 = r2 + O1O2
8 = r2 + √[(1 + 3)² + (5 - 1)²]
8 = r2 + 5
r2 = 3

Equation of C2 : (x - 1)² + (y - 5)² = 9
OR : x² + y² - 2x - 10y + 17 = 0