Chapter 8 - Section 8.4 - Plane Curves and Parametric Equations - 8.4 Exercises - Page 619: 58

$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1,~~x\geq0,~~y\geq0$

$x=a~\sqrt t$ $x^2=a^2t$ $t=\frac{x^2}{a^2},~~x\geq0$ $y=b~\sqrt {t+1}$ $y^2=b^2(t+1)$ $\frac{y^2}{b^2}=t+1,~~y\geq0$ $\frac{y^2}{b^2}=\frac{x^2}{a^2}+1$ $\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$