The lemniscate curve (x 2 + y 2 ) 2 = 4(x 2 y 2 )
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The lemniscate curve (x2 + y2)2 = 4(x2 − y2) was discovered by Jacob Bernoulli in 1694, who noted that it is “shaped like a figure 8, or a knot, or the bow of a ribbon.” Find the coordinates of the four points at which the tangent line is horizontal (Figure 14).
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1 -1 + 1
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