You have two points: (x1,y1) and (x2,y2)
The equation of an ellipse is (x - h)2 / a2  + (y - k)2 / b2 = 1
This has four unknowns and you have only 2 data points
i) (x1 - h)2 / a2  + (y1 - k)2 / b2 = 1
ii) (x2 - h)2 / a2  + (y2 - k)2 / b2 = 1
If we assume the ellipse has it centre at the origin then you have
i) x12 / a2  + y12 / b2 = 1
ii) x22 / a2  + y22 / b2 = 1
Two equations & two unknowns; some simple algebra get you a and b
Try setting up Solver to check you result
best wishes