Is it possible to determine a Conic given two points on the conic and equation of major and minor axis?
I choose $5$ random points on $\mathbb R^2$ independently. Since 5 points determine a conic, I get hold of a circle, parabola, ellipse or a hyperbola. Of course, it is most likely a hyperbola or an ellipse, probability of a parabola or circle is almost 0.
Now given two of these 5 points and equations of major, minor axis can I reach back to the ellipse/hyperbola?