Describe the graph of the polar equation.
-$$r = \frac { 3 } { 8 \cos \theta - \sin \theta }$$
A) Hyperbola passing through $( 3,8 )$
B) Line with slope 8 and $y$-intercept $( 0 , - 3 )$
C) Line with slope 3 and $y$-intercept $( 0 , - 8 )$
D) Ellipse centered at origin with intercepts $( \pm 8,0 )$ and $( 0 , \pm 1 )$

Question

Quizplus · Accepted Answer

To convert the given polar equation to Cartesian coordinates, we use the relations $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation, we get $x = \frac{3}{8 - y}$, which can be rearranged to $8x - y = 3$, a linear equation representing a line with a slope of 8 and a y-intercept of $(0, -3)$.

Describe the Graph of the Polar Equation r=38cos⁡θ−sin⁡θr = \frac { 3 } { 8 \cos \theta - \sin \theta }r=8cosθ−sinθ3​

Describe the Graph of the Polar Equation $r = \frac { 3 } { 8 \cos \theta - \sin \theta }$