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 Tuesday 30th of May

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# 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 (Â±2, 0) and (0, Â±1) in the x'y'-system, as shown in the figure below.