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henpen
Is there a general equation for all the conic sections? I assume there should be as if you get the equation for a cone and solve the simultaneous equation with it and the different types of plane, you'll get the conic sections of intersection.
yes there is:\[Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0\] Described in more detail here: http://math2.org/math/algebra/conics.htm