Find the polar coordinates of the point(s) of intersection of the given curves for 0 $0 \leq \theta < 2 \pi$
- $r = 4 \cos \theta , r = - 1 + 2 \cos \theta$

Question

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $$0 \leq \theta < 2 \pi$$
-$r = 4 \cos \theta , r = - 1 + 2 \cos \theta$
A) $\left( 2 , \frac { 2 \pi } { 3 } \right) , \left( - 2 , \frac { 4 \pi } { 3 } \right)$

B) $\left( 2 , \frac { 5 \pi } { 6 } \right) , \left( 2 , \frac { \pi } { 6 } \right)$

C) $\left\{ 2 , \frac { 2 \pi } { 3 } \right) , \left( 2 , \frac { 4 \pi } { 3 } \right)$

D) $\left\{ - 2 , \frac { 5 \pi } { 3 } \right) , \left( - 2 , \frac { \pi } { 3 } \right)$

Quizplus · Accepted Answer

To find the points of intersection, set the equations equal: $4 \cos \theta = -1 + 2 \cos \theta$. Solving gives $\cos \theta = -\frac{1}{2}$, which corresponds to $\theta = \frac{2\pi}{3}$ and $\theta = \frac{4\pi}{3}$. Substituting these into either equation gives $r = 2$ and $r = -2$, respectively.

Find the Polar Coordinates of the Point(s) of Intersection of the Given