How do you convert $r = 1 + cos (θ)$ $r=1+cos(theta)$ into cartesian form?

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Answer 1 · 2015-11-27T19:12:49

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

Multiply both sides by $r$ $r$ :

$r^{2} = r + r cos (θ)$ $r^2 = r+rcos(theta)$

Now, since $r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$ and $x = r cos (θ)$ $x=rcos(theta)$ , your equation becomes

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

How do you convert r=1+cos(theta)r=1+cos(θ)r=1+cos(theta) into cartesian form?