Intersection of a projective curve and a hyperplane

Question

Let $\mathcal{C}$ be a projective curve on $\mathbb{P}^2$ over a field $k$ defined by $\Phi(x,y,z)$ such that it is homogenization of an affine curve $\Phi(x,y)$. When we look at the intersection of $\mathcal{C}$ and the hyperplane defined by $\{ x=0 \}$, does it define an affine curve or a projective curve? To be more clear, the intersection of $\mathcal{C}$ and $\{ x=0\}$ will be defined by $\Phi(0,y,z)$ and it is homogenous. Since it has only 2 indeterminates, does it define a projective curve on $\mathbb{P}^2$? Or does it defines an affine curve?