The transformation x D a cosh u cos v, y D a sinh u sin v de
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The transformation x D a cosh u cos v, y D a sinh u sin v defines elliptical coordinates in the xy-plane. This coordinat
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The transformation x D a cosh u cos v, y D a sinh u sin v defines elliptical coordinates in the xy-plane. This coordinate system has singular points at x D ?a, y D 0. (a) Show that the v-curves, u = constant, are ellipses with foci at the singular points. (b) Show that the u-curves, v = constant, are hyperbolas with foci at the singular points. (c) Show that the u-curve and the v-curve through a nonsingular point intersect at right angles. (d) Find the scale factors hu and hv and the area element dA for the elliptical coordinate system.
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