Problem #144

A family of curves is given implicitly by

(x2 − 1)(y2 − 1) = λx2y2

with −1 ≤ x,y ≤ 1 and λ > 0. If λ is large, the curve is concave and if λ is small, the curve is convex (see figure below). For what value of λ does the transition from concave to convex occur?

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