inhomogeneous coordinates to homogeneous coordinates

Question

I will appreciate your help to solve this question.
For a function $fi:R^2 → R$ in inhomogeneous coordinates, we obtain a function
$fh : R^2$ × ($R$ \ {0}) $→ R$ in homogeneous coordinates as:
$fh(x, y, w) := fi(\frac xw, \frac yw)$.
Prove that:
(1) If $ fi(x, y) = 0$ is a bivariate polynomial equation, then $fh(x, y, w) = 0$ is a trivariate polynomial equation such that all monomials have the same degree.
(2) The equation $fi(x, y) = 0$ has at least one solution if and only if $fh(x, y, w) = 0$
Has infinitely many solutions.