Convert an Equation from Rectangular to Polar Coordinates
-$$( x - 12 ) ^ { 2 } + y ^ { 2 } = 144$$
A) $r = 24 \cos \theta$
B) $r = 24 \sin \theta$
C) $r ^ { 2 } = 24 \cos \theta$
D) $r = - 24 \sin \theta + 144$

Question

Quizplus · Accepted Answer

In polar coordinates, $x = r \cos \theta$ and $y = r \sin \theta$. Substituting these into the given equation, we get $(r \cos \theta - 12)^2 + (r \sin \theta)^2 = 144$. Simplifying, we find $r^2 - 24r \cos \theta + 144 = 144$, which simplifies further to $r^2 = 24r \cos \theta$, or $r = 24 \cos \theta$.

Convert an Equation from Rectangular to Polar Coordinates - (x−12)2+y2=144( x - 12 ) ^ { 2 } + y ^ { 2 } = 144(x−12)2+y2=144

Convert an Equation from Rectangular to Polar Coordinates
- $( x - 12 ) ^ { 2 } + y ^ { 2 } = 144$