$\text { Find a polar equation in the form } r \cos \left( \theta - \theta _ { 0 } \right) = r _ { 0 } \text { for the given line. }$
-$$y = - 4$$
A) $r \cos \theta = 4$
B) $r \cos \left( \theta + \frac { \pi } { 2 } \right) = 4$
C) $r \cos \left( \theta - \frac { \pi } { 2 } \right) = 4$
D) $r \cos ( \theta + \pi ) = 4$

Question

Quizplus · Accepted Answer

The equation $y = -4$ represents a horizontal line 4 units below the x-axis. In polar coordinates, this can be represented by moving $90^\circ$ or $\frac{\pi}{2}$ radians in the positive direction from the x-axis and then moving 4 units in the radial direction. Therefore, the correct polar equation is $r \cos \left( \theta + \frac { \pi } { 2 } \right) = 4$.

Find a polar equation in the form rcos⁡(θ−θ0)=r0 for the given line. \text { Find a polar equation in the form } r \cos \left( \theta - \theta _ { 0 } \right) = r _ { 0 } \text { for the given line. } Find a polar equation in the form rcos(θ−θ0​)=r0​ for the given line.

$\text { Find a polar equation in the form } r \cos \left( \theta - \theta _ { 0 } \right) = r _ { 0 } \text { for the given line. }$