Find a polar equation for the circle.
-$( x - 6 ) ^ { 2 } + y ^ { 2 } = 36$
A) $\mathrm { r } = - 12 \cos \theta$
B) $\mathbf { r } = 6 \cos \theta$
C) $r = 12 \cos \theta$
D) $r = 12 \sin \theta$

Question

Quizplus · Accepted Answer

To convert the given equation to polar format, we can substitute $x=r \cos 	heta$ and $y=r \sin 	heta$: $$(r\cos	heta-6)^2+r^2\sin^2	heta=36$$ Expanding and simplifying, we get: $$r^2-12r\cos	heta = 0$$ Dividing both sides by $r$ gives the polar equation $r=12\cos	heta$. Therefore, the correct choice is $	extbf{(C)}$.

Find a Polar Equation for the Circle (x−6)2+y2=36( x - 6 ) ^ { 2 } + y ^ { 2 } = 36(x−6)2+y2=36

Find a Polar Equation for the Circle $( x - 6 ) ^ { 2 } + y ^ { 2 } = 36$