Let $P$ be any point and let $OP=r$, where $O$ is the origin and let $OP$ make an angle $\theta$ with the axis, then $r$ and $\theta$ are called Polar coordinates of the point $P$, and the coordinates may be written as $(r,\theta)$.
Find the Cartesian equations of
[The $\cos\theta$ suggests the relation $x=r\cos\theta$, so multiply through by $r$.]
Therefore the Cartesian equation of $r=a(1+2\cos\theta) is
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