## Multivariable Calculus, 7th Edition

Cartesian equation: $y^2 - x =1$ --------
(a) $x= tan^2 \theta$ $-x = -tan^2 \theta$ $y = sec \theta$ $y^2 = sec^2 \theta$ Adding both equations: $y^2 - x =sec^2 \theta - tan^2 \theta$ $y^2 - x = \frac{1}{cos^2 \theta} - \frac{sin^2 \theta}{cos^2 \theta} = \frac{1 - sin^2 \theta}{cos^2 \theta}$ $y^2 -x = \frac{cos^2 \theta}{cos^2 \theta}$ $y^2 - x =1$ ----- (b) 1. Plot points determined by values for $\theta$ from $\frac{-\pi}{2}$ to $\frac {\pi} 2$ 2. Join them to produce a curve. 3. Draw an arrow indicating which direction the curve goes from $\theta = \frac{-\pi}{2}$ to $\theta = \frac{\pi}{2}$ ** Notice, from $\frac{-\pi} 2$ to 0, the curve goes from the right to the left, and between $0$ and $\frac{\pi}{2}$, it goes from left to right.