Rotating a Hyperbola
Write the equation xy - 1 = 0 in standard form.
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
the x'y'-system, as shown in the following figure.