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The equation is the bipolar equation of the Cayley's oval. Arthur Cayley (1821-1895) studied the curve in 1857. The curve is formed in nature as the equipotential lines 1)
in an electromagnetic or gravitational field.
And together in one field: 1) While the force is of the form F = k/r2, the potential has the form V=k/r. 2) Realize that r12 = (x+1)2 + y2, r22 = (x-1)2 + y2 |