Say, we got two hyperbolas:
Ax^2 + Bxy + Cy^2+ Dx + Ey + F = 0
Gx^2 + Hxy + Iy^2 + Jx + Ky + L = 0
Intersection\s can be solved by solving the above equations.
However, say the constants A, B, C, ... are some functions of other variables, say, T and U, each with their own range that they can possess. i.e. T +/- t and U +/- u.
I expect an area to be constructed where the intersection can lie on, instead of a perfect intersection( when t=0 and u=0). I intend to describe the area as an ellipse. Thus the problem changes to finding the major, minor and orientation of the ellipse.
Please provide advice on how this problem could be approached. Thanks!
What do you mean by area and ellipse when you're talking about intersections?