If a hyperbola is given by
$$\frac{y^2}{a^2}-\frac{x^2}{b^2} = 1$$
rewriting it as a function of x we have that
$$y(x) = a \sqrt{1+\frac{x^2}{b^2}}$$
is there a function $f(y)$ for which when I use it I will get a linear function on the graph $f(y)\space vs\space x$?