For the given rectangular equation, give its equivalent polar equation.
-$$2 x + 3 y = 6$$
A) $r = \frac { 2 \cos \theta + 3 \sin \theta } { 6 }$
B) $r = \frac { 2 \sin \theta + 3 \cos \theta } { 6 }$
C) $r = \frac { 6 } { 2 \sin \theta + 3 \cos \theta }$
D) $r = \frac { 6 } { 2 \cos \theta + 3 \sin \theta }$

Question

Quizplus · Accepted Answer

To convert the rectangular equation $2x + 3y = 6$ to a polar equation, we use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation yields $2(r\cos\theta) + 3(r\sin\theta) = 6$, which simplifies to $r(2\cos\theta + 3\sin\theta) = 6$, and finally to $r = \frac{6}{2\cos\theta + 3\sin\theta}$, which matches option D.

For the Given Rectangular Equation, Give Its Equivalent Polar Equation 2x+3y=62 x + 3 y = 62x+3y=6

For the Given Rectangular Equation, Give Its Equivalent Polar Equation $2 x + 3 y = 6$