It turns out that the shape of the cross-section of a fusee (https://en.wikipedia.org/wiki/Fusee_(horology)) is given by an equation of the form $y = a / \sqrt{x + b}$. I have read from many sources that the shape of a fusee is a hyperbola. Is the shape of the graph of this equation really a hyperbola? I mean this equation can be transformed into $xy^2 + by^2 - a = 0$ which is a cubic equation. Wouldn't the equation of a hyperbola be a quadratic equation?
If this equation describes a hyperbola, does it mean that $y = 1 / \sqrt{x}$ describes a hyperbola too? After all, we are just making $a = 1$ and $b = 0$.