Find the polar equation for the curve represented by the given Cartesian equation. $$x + y = 2$$
A) $r = 2 ( \cos \theta + \sin \theta )$
B)$r = \frac { 1 } { \cos \theta - \sin \theta }$
C)$r = \frac { 2 } { \cos \theta + \sin \theta }$
D)$r = \frac { 2 } { \cos \theta - \sin \theta }$
E) $r = 1 ( \cos \theta + \sin \theta )$

Question

Quizplus · Accepted Answer

We can convert the Cartesian equation to polar form as follows:
\begin{align*}
x+y&=2\
r\cos	heta+r\sin	heta&=2\
r(\cos	heta+\sin	heta)&=2\
r&=\frac{2}{\cos	heta+\sin	heta}
\end{align*}
Therefore, the polar equation is $r=\frac{2}{\cos	heta+\sin	heta}$, which matches choice $\boxed{	extbf{(C)}}$.

Find the Polar Equation for the Curve Represented by the Given