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$x^2 + xy + y^2 = 7$

$x$-axis = $\frac{\sqrt{21}}{3}$, $\frac{-2\sqrt{21}}{3}$

I don't understand how to find the $y$-axis.

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    Isn't the question asking you to find where the tangent to the curve $x^2+xy+y^2=7$ is horizontal and vertical?2012-11-14
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    If so, you can use implicit differentiation.2012-11-14
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    I tried that and got -2 sqrt 21/ 3, sqrt 21/ 3, which is the opposite of the x axis. Would that be correct?2012-11-14
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    Note that our curve function is **symmetric** in $x$ and $y$. By symmetry, for parallel to $y$-axis we interchange the roles of $x$ and $y$. Thus (i) your computation is correct and (ii) you need not have computed. If we **did not** have symmetry, the $x$-axis argument could be imitated by finding $\frac{dx}{dy}$.2012-11-14

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