You can easily construct a circle which has $A=(0, 0)$ as its center and two points $B$, $C$ of the same distance to $A=(0, 0)$ being located on it:
I wonder if it is possible to have an ellipse which also has $A=(0, 0)$ as its center, but intersecting two points $B$, $C$ which have not the same distance from $(0, 0)$. The foci of the ellipse should be parallel to the two points which should intersect the ellipse. Sketching the solution, it should look somewhat as follows:
How would you create an ellipse equation in terms of $B$ and $C$?