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1. 6-7 A New Look at
Conic Sections
Objective:
Classify second-degree equations.

2. Degenerate Conics
Degenerate (adj.):
 having lost the physical, mental, or
moral qualities considered normal
and desirable; showing evidence of
decline.
 lacking some property, order, or
distinctness of structure previously
or usually present, in particular.

4. General Form
Ax2 + Bxy + Cy2 +Dx +Ey + F = 0
(where A, B, and C are not all 0)

5. The Discriminant
If B2 – 4AC is:
◦< 0 and A = C, B = 0  circle
◦< 0 and A ≠ C  ellipse
◦= 0  parabola
◦> 0  hyperbola
(As long as graph is not degenerate.)

6. Example:
Identify the graph of the
equation x2 – 2xy + 3y2 – 1 = 0

7. More Examples:
4x2 + 4xy – y2 = 16
x2 – 6xy + 9y2 + x – y – 1 = 0