Chapter 11: Parametric Equations and Polar Coordinates - Practice Exercises - Page 688: 36

$r=-4 \cos \theta$

Consider $x^2+y^2+4x=0$ or, $(x+2)^2+y^2=4$ Here, we get the equation of a circle with center $(-2,0)$ and radius $2$ This implies that $r^2+4r \cos \theta=0 \implies r^2=-4r \cos \theta $ Hence, $r=-4 \cos \theta$