# Does the equation $x^2y^2=5$ have any inflection point?

Does the equation $x^2y^2=5$ have any inflection point and find it?

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I textify the equation. Check if this is what you would like to ask. –  Paul Dec 16 '11 at 23:57
The equation $x^2y^2=5$ determines the same set of points in the plane as $$xy=\sqrt5\;\text{ OR }\;xy=-\sqrt5\;.$$ What do the graphs of $xy=\sqrt5$ and $xy=-\sqrt5$ look like? Do they have any inflection points?
@Victor: You don’t need any multivariate calculus for this problem: it’s just ordinary calculus of one variable. Neither $y=\sqrt{5}/x$ nor $y=-\sqrt{5}/x$ has any inflection points, because their second derivatives are never $0$, so $x^2y^2=5$ also has no inflection points. –  Brian M. Scott Dec 17 '11 at 0:56