math
posted by wong .
a straight line passing through the origin with slope m cuts the circle x^2+y^24x2y4=0 at A(a,b) and B(b,c).
A. Find a quadratic equation whose roots are a and c
ans: (1+m^2)x^2(2m+4)x4=0
B. if P is the midpoint 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?
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