Chapter 10 - Section 10.6 - Conics in Polar Coordinates - Exercises - Page 592: 52

$r \cos \theta=-4$

Conversion of polar coordinates and Cartesian coordinates are as follows: a) $r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$ b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ c) $x=r \cos \theta$ d) $y=r \sin \theta$ We are given that $x=-4$ This implies that $r \cos \theta=-4$ Thus, $r \cos \theta=-4$