\(\displaystyle{r}^{{{2}}}=-{4}{r}{\cos{\theta}}\)

Hence, \(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}=-{4}{x}\)

Hence,\(\displaystyle{x}^{{{2}}}+{4}{x}+{y}^{{{2}}}={0}\)

Or,\(\displaystyle{x}^{{{2}}}+{4}{x}+{y}^{{{2}}}+{4}={0}+{4}={4}\)

Or, \(\displaystyle{\left({x}+{2}\right)}^{{{2}}}+{y}^2={2}^{{{2}}}\)

Hence, the equivalent cartesian equation:\(\displaystyle{\left({x}+{2}\right)}^{{{2}}}+{y}^{{{2}}}={2}^{{{2}}}\)

And it represents the circle of radius 2 centred at (-2, 0)