Comment by amavect

Actually, yes! We can use homogenous-degree-1 (provable from the homomorphism) to prove it.

  F(r,q0,q1)
  = F(r,q0*1,q1*1)
  = q0*q1*F(r,1,1)

Very simple! It remains to show that F(r,1,1) = K/r^2, as intended.