(a)
The graph drawn is a circle
passing through A, B, C
(b)
Let P be the centre
ACB is the angle at circumference
APB is the angle at centre
APB = 2ACB = 60°
As AP = BP (radii), APB is equil.
Let P = (m,n)
Set two eqs using distance formula
Solving, (m,n) = (0,4) or (sqrt3, 1)
As radius = 2, required equations are
x^2 + (y-4)^2 = 4
or (x-sqrt3)^2 + (y-1)^2 = 4