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General Conic Section - Which cone/plane create the curve?

For any general conic section defined by Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, this applet gives you a cone and a plane whose intersection gives the same curve. For non-degenerate cases, the type of conic curve is identified (ellipse, parabola, hyperbola). Admittedly, degenerate cases (points, parallel lines, intersecting lines) are not detected, yet the world keeps turning!