Question Number 217299 by peter frank last updated on 09/Mar/25
Answered by mr W last updated on 10/Mar/25
$${x}={r}\:\mathrm{cos}\:\theta \\ $$$${y}={r}\:\mathrm{sin}\:\theta \\ $$$$\left({r}\:\mathrm{cos}\:\theta−\mathrm{1}\right)^{\mathrm{2}} +\left({r}\:\mathrm{sin}\:\theta\right)^{\mathrm{2}} =\mathrm{16} \\ $$$${r}^{\mathrm{2}} −\mathrm{2}\:\mathrm{cos}\:\theta\:{r}−\mathrm{15}=\mathrm{0} \\ $$$$\Rightarrow{r}=\mathrm{cos}\:\theta\pm\sqrt{\mathrm{cos}^{\mathrm{2}} \:\theta+\mathrm{15}}\:\checkmark \\ $$