 To apply this to algebraic curves, write "f"("x", "y") as
where each "u""r" is the sum of all terms of degree "r".The homogeneous equation of the curve is then
Applying the equation above and setting "z"=1 produces
as the equation of the tangent line.The equation in this form is often simpler to use in practice since no further simplification is needed after it is applied.