I'm trying to graph a function that has a parameter $a$ with the help of its first derivative.
$$f(x) = x * \sqrt{\frac{x+a}{x-a}} \qquad a>0$$
I've managed to determine domain, derivative, stationary points and intervals where the function is falling and rising. I've calculated the asymptote and determined it to be
$$ y = x + a$$
The only thing left to do is to see in which point does the function cross its asymptote.
$$ x + a = x * \sqrt{\frac{x+a}{x-a}} $$
From this it follows that $a = 0$. I don't know how to interpret this result, or what does it mean for the graph. I've checked in $Mathematica$ and it appears the point where graph touches the asymptote is in $-a$. I don't quite understand that conclusion.
