Editing Polar coordinate system (section)

===Circle===
[[Image:circle r=1.svg|thumb|right|A circle with equation {{math|1=''r''(''φ'') = 1}}]]
The general equation for a circle with a center at <math>(r_0, \gamma)</math> and radius ''a'' is
<math display="block">r^2 - 2 r r_0 \cos(\varphi - \gamma) + r_0^2 = a^2.</math>

This can be simplified in various ways, to conform to more specific cases, such as the equation
<math display="block">r(\varphi)=a </math>
for a circle with a center at the pole and radius ''a''.<ref name="ping">{{Cite web |last=Claeys |first=Johan |title=Polar coordinates |url=http://www.ping.be/~ping1339/polar.htm |url-status=dead |archive-url=https://web.archive.org/web/20060427230725/http://www.ping.be/~ping1339/polar.htm |archive-date=2006-04-27 |access-date=2006-05-25}}</ref>

When {{math|1=''r''<sub>0</sub> = ''a''}} or the origin lies on the circle, the equation becomes
<math display="block">r = 2 a\cos(\varphi - \gamma).</math>

In the general case, the equation can be solved for {{math|''r''}}, giving
<math display="block">r = r_0 \cos(\varphi - \gamma) + \sqrt{a^2 - r_0^2 \sin^2(\varphi - \gamma)}</math>
The solution with a minus sign in front of the square root gives the same curve.<!-- Better rephrasing? -->