Chapter 13 - Vector Geometry - 13.7 Cylindrical and Spherical Coordinates - Exercises - Page 700: 29

$$ r= z\sec \theta \tan \theta .$$

Since $$ x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$ then $\dfrac{x^2}{yz}=1$ takes the form $$\frac{ r^2\cos^2\theta}{z r\sin\theta } =1\Longrightarrow r=\frac{z\sin\theta}{\cos^2\theta}=z\sec \theta \tan \theta .$$