Polar coordinate system
Circle

The general equation for a circle with a center at (r 0, γ) {\displaystyle (r_{0},\gamma)} and radius a is r 2 − 2 r r 0 cos (φ − γ) + r 0 2 = a 2. {\displaystyle r^{2}-2rr_{0}\cos(\varphi -\gamma)+r_{0}^{2}=a^{2}.}

This can be simplified in various ways, to conform to more specific cases, such as the equation r (φ) = a {\displaystyle r(\varphi)=a} for a circle with a center at the pole and radius a.

When r = a or the origin lies on the circle, the equation becomes r = 2 a cos (φ − γ). {\displaystyle r=2a\cos(\varphi -\gamma).}

In the general case, the equation can be solved for r, giving r = r 0 cos (φ − γ) + a 2 − r 0 2 sin 2 (φ − γ) {\displaystyle r=r_{0}\cos(\varphi -\gamma)+{\sqrt {a^{2}-r_{0}^{2}\sin ^{2}(\varphi -\gamma)}}} The solution with a minus sign in front of the square root gives the same curve.
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