Answer
$ r=4\sec\theta$
Work Step by Step
Formulas relating rectangular $(x,y)$ and polar $(r,\theta)$ coordinates:
$ x=r\cos\theta$ and $ y=r\sin\theta$
$r^{2}=x^{2}+y^{2}$ and $\displaystyle \tan\theta=\frac{y}{x}$.
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$x=4 $
Substitute $ r\cos\theta$ for $x.$
$r\cos\theta=4 \qquad/\div\cos\theta$
$r=\displaystyle \frac{4}{\cos\theta}$
$ r=4\sec\theta$
