The evolute of a hyperbola with parametric equations
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(1)
|
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(2)
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is
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(3)
|
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(4)
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which is similar to a Lamé curve, but with a minus sign. Eliminating 
gives the implicit Cartesian equation for the evolute as
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(5)
|
From a point between the two branches of the evolute, two normals can be drawn to the hyperbola. However, from a point beyond the evolute, four normals can be drawn.
