The question asks to find the slopes to tangent lines of the following curve:

$$ y^4 - 4y^2 = x^4 - 9x^2 $$

at the point (0,0).

It's easy to see that differentiating implicitly doesn't help, as we get the form $\frac{0}{0}$. Is there any other way I can solve this?


A start: Note that when division is allowed, we have $\frac{y^2}{x^2}=\frac{x^2-9}{y^2-4}$. So as we travel along the curve towards $(0,0)$, $\frac{y^2}{x^2}$ approaches $\frac{9}{4}$.


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