How to find the radius(major and minor) with the given 3 points in an ellipse?

Question

I have 3 random points in an ellipse. Is it possible to find the radius of the ellipse?

Answer 1

The equation of an ellipse whose major and minor axes are parallel to the Cartesian axes is:

$$ \left(\frac{x-x_{0}}{a}\right)^{2}+\left(\frac{y-y_{0}}{b}\right)^{2}=1 $$

As you can see, the equation contains 4 different variables. Therefore, 3 points aren't sufficient to uniquely identify the ellipse.