Chapter 10 - Section 10.1 - Parametrizations of Plane Curves - Exercises - Page 563: 32

$x=\cot^2 \theta$;$y= \cot \theta$; $0\leq \theta \leq \dfrac{\pi}{2}$

Here, $y=\sqrt x$ We know that $y=x \tan \theta$ Then, we have $\sqrt x= \cot \theta$ This implies that $x=\cot^2 \theta$ Now, $y=(\cot^2 \theta) (\tan \theta) \implies y= \cot \theta$ Hence, $x=\cot^2 \theta$;$y= \cot \theta$; $0\leq \theta \leq \dfrac{\pi}{2}$