If $f: \mathbb CP^2 \rightarrow \mathbb CP^2$ is a homeomorphism, then $f(\mathbb CP^1)$ intersects $\mathbb CP^1$

Question

Consider the standard embedding $\mathbb CP^1 \subseteq \mathbb CP^2$.
Let $f : \mathbb CP^2 \rightarrow \mathbb CP^2$ be a homeomorphism. The goal is to show that $f(\mathbb CP^1)$ always intersects $\mathbb CP^1$.

I am not sure how to start this problem.
I would appreciate any help or hint, for example, some relevant chapters/theorems from Hatcher.