Describe the graph of the polar equation.
-$$r ^ { 2 } + 2 r ^ { 2 } \sin \theta \cos \theta = 144$$
A) Two horizontal lines passing through $( 0 , \pm 12 )$
B) Parabola opening upward with vertex at $( 0,12 )$
C) Two straight lines of slope $- 1$, y-intercepts $( 0 , \pm 12 )$
D) Parabola opening to the right with vertex at $( 12,0 )$

Question

Quizplus · Accepted Answer

The given equation can be simplified using the double angle identity for sine, $2\sin\theta\cos\theta = \sin(2\theta)$, and converting to Cartesian coordinates with $r^2 = x^2 + y^2$ and $y/x = \tan(\theta)$. This leads to lines with slope -1 and y-intercepts at $\pm 12$.

Describe the Graph of the Polar Equation r2+2r2sin⁡θcos⁡θ=144r ^ { 2 } + 2 r ^ { 2 } \sin \theta \cos \theta = 144r2+2r2sinθcosθ=144

Describe the Graph of the Polar Equation $r ^ { 2 } + 2 r ^ { 2 } \sin \theta \cos \theta = 144$