Recall that except for degenerate cases, the graph of Ax2 + Bxy + Cy2 + Dx + Ey + F = 0...

Recall that except for degenerate cases, the graph of Ax² + Bxy + Cy² + Dx + Ey + F = 0 is

(a) Prove that the graph of the equation is an ellipse whenever A > C > B > 0.

(b) Prove that the graph of the equation is a hyperbola if AC < 0 or B < C < 4A < 0.

(c) Prove that if the graph is a parabola, then BC = 0 or A = B²/(4C).