The polar equation that corresponds to the rectangular equation $2 x + y = 4$ is

A) $r = \frac { 4 } { 2 \cos \theta + \sin \theta }$
B) $r = \frac { 4 } { 2 \cos \theta - \sin \theta }$
C) $r = \frac { 4 } { \cos \theta + 2 \sin \theta }$
D) $r = \frac { 4 } { \cos \theta - 2 \sin \theta }$
E) $r = \frac { - 4 } { 2 \cos \theta + \sin \theta }$

Question

The polar equation that corresponds to the rectangular equation $2 x + y = 4$ is

A) $r = \frac { 4 } { 2 \cos \theta + \sin \theta }$
B) $r = \frac { 4 } { 2 \cos \theta - \sin \theta }$
C) $r = \frac { 4 } { \cos \theta + 2 \sin \theta }$
D) $r = \frac { 4 } { \cos \theta - 2 \sin \theta }$
E) $r = \frac { - 4 } { 2 \cos \theta + \sin \theta }$

Quizplus · Accepted Answer

To convert the rectangular equation $2x + y = 4$ to a polar equation, use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation yields $2r\cos\theta + r\sin\theta = 4$, which simplifies to $r = \frac{4}{2\cos\theta + \sin\theta}$.

The Polar Equation That Corresponds to the Rectangular Equation 2x+y=42 x + y = 42x+y=4

The Polar Equation That Corresponds to the Rectangular Equation $2 x + y = 4$