# 21.9 Rotation of Axes

**Angle of Rotation of Axes • Eliminating the**${B}^{2}\hspace{0.17em}-\hspace{0.17em}4AC$*xy*-term • Value of**Determines Curve**

In this chapter, we have discussed the circle, parabola, ellipse, and hyperbola, and in the last section, we showed how these curves are represented by the second-degree equation

**(21.34)**

The discussion of these curves included their equations with the center (vertex of a parabola) at the origin. However, as noted in the last section, except for the special case of the hyperbola $xy\hspace{0.17em}=\hspace{0.17em}c\hspace{0.17em},\hspace{0.17em}$ we did not show what happens when the axes are *rotated* about the origin.

*If a set of axes is rotated about the origin through an angle* $\theta \hspace{0.17em},\hspace{0.17em}$ *as shown in Fig. 21.97, we say that there has been a* **rotation of axes.**

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