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Published online by Cambridge University Press: 15 February 2024
The following equations relate y only implicitly to x:(1)(2) In both equations, y is a function of x for a continuous range of (x, y) values in the real x-y plane. (1) represents an ellipse. (2) has been designed by the author to have a solution in the real x-y plane at (−1, 2), and because the function on the left-hand side of (2) meets certain conditions regarding continuity and partial differentiability there must be a line of points in the real x-y plane satisfying (2) and passing continuously through (−1, 2) [1, pp. 23-28].