Question: Prove that the graph of the equation Ax2 + Cy2 + Dx + Ey + F = 0 is one of the following (except in

Prove that the graph of the equation
Ax2 + Cy2 + Dx + Ey + F = 0
is one of the following (except in degenerate cases).
Conic .................................................... Condition
(a) Circle .............................................. A = C, A ≠ 0
(b) Parabola .......................................... A = 0 or C = 0, but not both
(c) Ellipse ............................................. AC > 0, A ≠ C
(d) Hyperbola ........................................ AC < 0

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Ax 2 Cy 2 Dx Ey F 0 Assume that the conic is not degenerate a A C A 0 Ax 2 Ay 2 Dx Ey F 0 x 2 y 2 DA ... View full answer

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