Chapter 11: Parametric Equations and Polar Coordinates - Section 11.7 - Conics in Polar Coordinates - Exercises 11.7 - Page 686: 52

$r \cos \theta=-4$

The conversion of polar coordinates and Cartesian coordinates are described as follows: 1. $r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$ 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: $x=-4$ Then, we have $r \cos \theta=-4$ Hence, $r \cos \theta=-4$