Rotating an Ellipse
Sketch the graph of
Solution
Because A = 7,
and
C = 13, you have (for 0 θ < π/2)
Therefore, the equation in the x'y'-system is derived by making the following
substitutions.
Substituting these expressions into the original equation eventually simplifies (after
considerable algebra) to
This is the equation of an ellipse centered at the origin with vertices at (±2,
0) and (0, ±1)
in the x'y'-system, as shown in the figure below.
