How do you graph the polar equation $r = 3 + 3 cos θ$ $r=3+3costheta$ ?

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Answer 1 · 2018-03-22T10:14:10

${(x^{2} + y^{2} - 3 x)}^{2} = 9 x^{2} + 9 y^{2}$ $(x^2+y^2-3x)^2=9x^2+9y^2$

Multiply each term by $r$ $r$ to get:
$r^{2} = 3 r + 3 r cos θ$ $r^2=3r+3rcostheta$

$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$
$r cos θ = x$ $rcostheta=x$

$x^{2} + y^{2} = 3 \sqrt{x^{2} + y^{2}} + 3 x$ $x^2+y^2=3sqrt(x^2+y^2)+3x$

${(x^{2} + y^{2} - 3 x)}^{2} = 9 x^{2} + 9 y^{2}$ $(x^2+y^2-3x)^2=9x^2+9y^2$

How do you graph the polar equation r=3+3cosθr=3+3costheta?