Answer
Cartesian equation: $y^2 - x =1$
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Work Step by Step
(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} $
$y^2 -x = \frac{cos^2 \theta}{cos^2 \theta}$
$y^2 - x =1$
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(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.
