Wotzdorfg

2021-09-03

Find polar equation for the circle. Sketch circle in the coordinate plane and label it with both its Cartesian and polar equations. ${x}^{2}+2x+{y}^{2}=0$

Lacey-May Snyder

Skilled2021-09-04Added 88 answers

Given that:

${x}^{2}+{y}^{2}+2x=0$

Converting polar coordinates from Cartesian coordinates

$x=r\mathrm{cos}\left(\theta \right)\u200a\u200a,\u200a\u200a\u200a\u200a\u200ay=r\mathrm{sin}\left(\theta \right){x}^{2}+{y}^{2}={r}^{2}$

${x}^{2}+{y}^{2}+2x=0$

${r}^{2}+2r\mathrm{cos}\left(\theta \right)=0$

$r(r+2\mathrm{cos}\left(\theta \right))=0$

r=0

$r+2\mathrm{cos}\left(\theta \right)=0$

$r=-2\mathrm{cos}\left(\theta \right)$

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