21.9 Rotation of Axes

  • Angle of Rotation of Axes • Eliminating the xy-term • Value of B2 − 4AC 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

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 (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 = c ,  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 θ ,  as shown in Fig. 21.97, we say that there has been a rotation of axes.

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