Replace the polar equation with an equivalent Cartesian equation.
-$$r = \frac { 1 } { 5 \cos \theta - 3 \sin \theta }$$
A) $\frac { x } { 5 } + \frac { y } { 3 } = 1$
B) $5 y - 3 x = 1$
C) $5 x - 3 y = 1$
D) $\frac { 1 } { 5 x - 3 y } = 1$

Question

Quizplus · Accepted Answer

We can use the relationships $x=r\cos	heta$ and $y=r\sin	heta$ to get:
\begin{align*}
r &= \frac{1}{5\cos	heta-3\sin	heta} \
r(5\cos	heta-3\sin	heta) &= 1 \
5r\cos	heta - 3r\sin	heta &= 1 \
5(x) - 3(y) &= 1 \
5x-3y &= 1
\end{align*} Thus, the Cartesian equivalent of the polar equation is $5x-3y=1$, or choice $\boxed{	extbf{(C)}}$.

Replace the Polar Equation with an Equivalent Cartesian Equation r=15cos⁡θ−3sin⁡θr = \frac { 1 } { 5 \cos \theta - 3 \sin \theta }r=5cosθ−3sinθ1​

Replace the Polar Equation with an Equivalent Cartesian Equation $r = \frac { 1 } { 5 \cos \theta - 3 \sin \theta }$