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Home Limits, Analytic Geometry, and Approximations Rotation of Axes Examples Example 2
 
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Example 2

Sketch the curve xy - 4 = 0.

Step 1

Apply the Discriminant Test to find the type of curve.

B2 - 4AC = 12 - 4 · 0 · 0 = 1.

The discriminant is positive, so the curve is a hyperbola.
Step 2

Find an angle α with

05_limits_g_approx-377.gif
Step 3

Change coordinate axes using the rotation equations.

05_limits_g_approx-378.gif

Substituting, we get

05_limits_g_approx-380.gif

As a check, the discriminant is still 02 - 4 · (½) · ( - ½) = 1.
Step 4

Draw the X and Y axes as dotted lines and sketch the curve.

The new axes are found by rotating the old axes by α = 45°. The curve is shown in Figure 5.7.5.

05_limits_g_approx-381.gif

Figure 5.7.5: Example 2: xy - 4 = 0
Home Limits, Analytic Geometry, and Approximations Rotation of Axes Examples Example 2

Last Update: 2006-11-15