Equation representing the branch of hyperbola Is there an equation representing the one branch of hyperbola ($x^2-y^2=1$). This is the regular hyperbola: ![enter image description here]( This is the expected curve: ![enter image description here](

In order to "exclude" possible negative $x$ we can do the trick of taking the square root, since this is not possible for negative numbers, then cancel the square root by using a square. Thus the equation will be identical as the one above, but only defined on the positive numbers for $x$.

$$(\sqrt x^2)^2 - y^2 = 1$$

Note that we could in a similar way get only the "left" part of the curve, with negative $x$ values, by putting a minus sign on $x$, i.e.

$$(\sqrt{ -x}^2)^2 - y^2 = 1$$