Prove that the graph of the equation Ax2 + Cy2 + Dx + Ey + F = 0 is one of the following

Chapter 10, Problem 75

(choose chapter or problem)

Proof   Prove that the graph of the equation

\(Ax^2 + Cy^2 + Dx + Ey + F = 0 \)

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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