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Elementary Calculus Limits, Analytic Geometry, and Approximations Rotation of Axes Method of Rotation of Axes
 

Method of Rotation of Axes

When to Use To graph an equation of the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 where B is nonzero.

Step 1 Use the Discriminant Test to determine the type of curve.
Step 2

Find an angle α with

05_limits_g_approx-382.gif
Step 3

Change coordinate axes using the Rotation Equations. The new equation has the form

A1X2 + CY2 + D1X + E1Y + F1 = 0,

where

x = X cos α. - Y sin α, y = X sin α + Y cos α.
Step 4 Draw the X- and Y-axes by rotating the old axes through the angle α. The curve can now be sketched by our previous method, using Translation of Axes if necessary.

Last Update: 2006-Nov-25