Proof Prove that the graph of the equation is one of the following (except in degenerate

Chapter 10, Problem 90

(choose chapter or problem)

Prove that the graph of the equation

\(A x^{2}+C y^{2}+D x+E y+F=0\)

is one of the following (except in degenerate cases).

Conic                                                      Condition

(a) Circle                                                 A = C

(b) Parabola                                            A = 0 or C = 0 (but not both)

(c) Ellipse                                                AC > 0

(d) Hyperbola                                           AC < 0

Text Transcription:

Ax^2 + Cy^2 + Dx + Ey + F = 0

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