There are several different graphs and equations for the polar graph. For circles at the origin the equation is r=a and |a|=radius and the equation for spirals is r=atheta. For circles with a center on an axis the equations are r=asintheta; r=acostheta and a=diameter. The equations for cardiods are r=a+asintheta; r=a-sintheta; r=a+acostheta; r=a-costheta. Limacons have a similar equation with it being r=a+bsintheta; r=a-bsintheta; r=a+bcostheta; r=a-bcostheta when a/b is less than 1. The equation for rose curves are r=asin(n)theta and r=acos(n)theta and an odd n means n is the number of petal while an even n means that 2n equals the number of petals. Lastly the equations for lemniscates are r^2=acos2theta and r^2=asin2theta. Here is a picture of some of the graphs of polar equations. 
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