# Replace the polar equations with equivalent. Cartesian equations. Then describe or identify the graph. r^{2} = -4r cos theta

Replace the polar equations with equivalent
Cartesian equations. Then describe or identify the graph. $$\displaystyle{r}^{{{2}}}=-{4}{r}{\cos{\theta}}$$

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

davonliefI

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

###### Have a similar question?
content_user

Answer is given below (on video)