# 21.8 The Second-degree Equation

**Second-degree Equation • Coefficients**`A`,`B`,`C`Determine the Type of Curve • Conic Sections

The equations of the circle, parabola, ellipse, and hyperbola are all special cases of the same general equation. In this section, we discuss this equation and how to identify the particular form it takes when it represents a specific type of curve.

*Each of these curves can be represented by a* **second-degree equation** *of the form*

**(21.34)**

The coefficients of the second-degree equation terms determine the type of curve that results. Recalling the discussions of the general forms of the equations of the circle, parabola, ellipse, and hyperbola from the previous sections of this chapter,

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