Curve of all points C for which $|AC|=|BC|$ and $BC \parallel g$ ...?

Question

sorry for the title being a little bit weird. The full question is:

Let's take two non parallel lines $g$ and $h$ and a fixed(!) point $A \not \in g$. Now take a look at all triangles $ABC$ for which:

• $|AC|=|BC|$
• $B \in g$
• $|BC| \parallel h$

Is there a specific curve of all those points C? I'd like to get a visualization of them wit GeoGebra and already tried, however I was not capable of finising it (maybe you've got some advice for me).

Thank you!