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

UkusakazaL 2021-09-14 Answered
Replace the polar equations with equivalent
Cartesian equations. Then describe or identify the graph. \(\displaystyle{r}^{{{2}}}=-{4}{r}{\cos{\theta}}\)

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Expert Answer

davonliefI
Answered 2021-09-15 Author has 14327 answers

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

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