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4. transform each polar equation to an equation in rectangular coordinates and identify its shape.
a. r=6
b. r=2cos theta

well, you know that r cos (theta) is the same as x, so:  

a) is simply x = 4 and that is a line.  

With b), multiply either side by r, so:  

r^2 = 6 r sin (theta), then we know that r sin (theta) is the same as y:  

r^2 = 6y, and we also know r^2 = x^2 + y^2, therefore:  

x^2 +y^2 = 6y, that is rectangular...  

So:  

a) x = 4  

b) x^2 +y^2 - 6y = 0  

Actually, for b you could always complete the square...  

x^2 + y^2 - 6y + 9 = 9  

x^2 + (y - 3)^2 = 9  

This would make a circle

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