The evolute of a hyperbola with parametric equations
(1)
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(2)
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is
(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
(5)
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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.