<s>[INST] Finding the asymptotes of $(y-a)^2(x^2-a^2)=x^4+a^4$. Problem: Finding the  asymptotes of $(y-a)^2(x^2-a^2)=x^4+a^4$.  
My efforts:  $(y-a)^2(x^2-a^2)=x^4+a^4\implies (y-a)^2=\dfrac{x^4+a^4}{x^2-a^2}\implies x=\pm a$ are vertical asymptotes. What are the remaining asymptotes?
 [/INST] Rewrite the equation as
$$y=a \pm \sqrt{\frac{x^4+a^4}{x^2-a^2}}$$
The vertical asymptotes $x=\pm a $ are directly identified. Since 
$$\lim_{x^2\to\infty} y(x) = a\pm x$$
$y=a\pm x $ are the slant asymptotes.
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