Suppose we have a quadratic polynomial equation in two variables:
$$p(x,y) = ax^2 + by^2 + cxy + dx + ey + f = 0$$
Under which conditions does at least one solution $p(x,y)=0$ exist with $x$ and $y$ both real and positive?
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I know how to answer the question for a quadratic in one variable, so I have tried to reduce this problem to that problem, but so far unsuccessfully. – Jules Sep 16 '15 at 19:35
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Have you tried to study the two variables function $p$ and finding a condition on the parameters so that the minimum and maximum are of different signs? – PAM Oct 21 '15 at 09:44