Question

Find a Cartesian equation for the curve and identify it. r = 6 tan θ sec θ

Answer 1

\[\begin{align*}
r&=6\tan\theta\sec\theta\\\\
r&=\frac{6\dfrac{\sin\theta}{\cos\theta}}{\cos\theta}\\\\
r\cos\theta&=6\frac{\sin\theta}{\cos\theta}\\\\
r\cos\theta&=6\frac{\sin\theta}{\cos\theta}\cdot\frac{r}{r}\\\\
x&=6\frac{y}{x}\\\\
y&=\frac{1}{6}x^2
\end{align*}\]