Answer
$r=7 \sec \theta$
Work Step by Step
The conversion of polar coordinates and Cartesian coordinates are described as follows:
1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$
2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
3. $x=r \cos \theta$ and 4. $y=r \sin \theta$
Given: $r \cos \theta=7$
This implies that $r=(7)(\dfrac{1}{\cos \theta})$
Hence, $r=7 \sec \theta$
