Question 980071
Identities Used



r^2 = x^2 + y^2
x = r*cos(theta)



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r= -16cos(theta)



r*r= r*(-16cos(theta)) ... multiply both sides by r



r^2 = -16(rcos(theta))



r^2 = -16x ... replace "rcos(theta)" with x (see above)



x^2 + y^2 = -16x ... replace r^2 with x^2+y^2 (see above)



x^2+16x + y^2 = 0



x^2+16x +64 + y^2 = 0+64 ... see note below



(x^2+16x +64) + y^2 = 64



(x+8)^2 + y^2 = 64



This is a circle with center (-8,0) and radius 8



Note: I took half of the x coefficient (16) to get 8. Then I squared 8 to get 64. I added 64 to both sides. This is all done to complete the square.