Rotating a Hyperbola
Write the equation xy - 1 = 0 in standard form.
Solution
Because A = 0, B = 1, and C = 0, you have (for 0
θ < π/2)
The equation in the x'y'-system is obtained by making the following substitutions.
Substituting these expressions into the equation xy - 1 = 0 produces
This is the equation of a hyperbola centered at the origin with vertices at
 in
the x'y'-system, as shown in the following figure.
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