a straight line passing through the origin with slope m cuts the circle x^2+y^2-4x-2y-4=0 at A(a,b) and B(b,c).

Question

A. Find a quadratic equation whose roots are a and c
ans: (1+m^2)x^2-(2m+4)x-4=0

B. if P is the mid-point of AB, find the coordinates of P in terms of m.
ans: P= (m+2)/(1+m^2), (m(m+2))/(1+m^2)

C. as m varies, the locus of P is part of a curve C. Find the equation of C.
ans: x^2+y^2=2x+y

I know how to do question A and question B, but how to do C? any idea?