I know it's a very simple question, but I do not know any equation that helps me with this thing, $$C=(-3,1); \ \ V_1=(-6,1); \ \ V_2=(0,1)$$
In my opinion, I'm missing the size of the straight side or the eccentricity. But I ask in case anyone knows any equation that I do not know. But I ask in case anyone knows any equation that I do not know.
You are correct.
A generic ellipse has 5 degrees of freedom, roughly speaking 5 numbers to be chosen independently. Theoretically your three points provide two coordinates each, amounting to 6 degrees of information. But $C$ is completely defined as the midpoint between $V_1$ and $V_2$, so knowing its coordinates adds no new information. The two vertices alone still leave room for one parameter, i.e. you have a one-parameter family of ellipses with these two vertices.
You could take the minor semi-axis to describe this remaining parameter, or the eccentricity, or focal distance, or a lot of other possible parametrizations, depending on use case and taste.