Level curves for the sum of the squares of the normals to an ellipse |
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| Authors: | John Lekner |
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| Institution: | 1. The MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Chemical and Physical Sciences, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
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| Abstract: | The squares of the normals to an ellipse are shown to be determined by a quartic. It follows from the properties of that quartic that the sum of the squares of the normals from a point remains constant as this point moves on one of a family of conjugate ellipses or hyperbolas. Likewise the sum of the squares of the normals to a hyperbola from any point on a conjugate ellipse is a constant. |
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