If, with y a function of x, I have the equation x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}-5xy+3y^{2}= 7, then by implicit differentiation, I get that dy/dx = (2x-5y)/(5x-6y). This equals zero everywhere on the straight line y=(2/5)x except at the origin. This would seem to indicate stationary points everywhere on that line, which is hard to imagine, and anyway the graph of this equation seems to be a hyperbola, having no stationary points. Obviously I am missing something very basic here. Any help would be appreciated.

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# Implicit differentiation gives too many stationary points

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