Which answer is a polar form of the given rectangular equation?
$$16 x y = 144$$
A) $r ^ { 2 } = 9 \sec \theta \csc \theta$
B) $r ^ { 2 } = 3 \sec \theta \csc \theta$
C) $r ^ { 2 } = 3 \sin \theta \cos \theta$
D) $r ^ { 2 } = 9 \sin \theta \cos \theta$
E) $\theta = 9 \sin \theta \cos \theta$

Question

Quizplus · Accepted Answer

To convert the given rectangular equation $16xy = 144$ to polar form, use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the equation gives $16(r\cos\theta)(r\sin\theta) = 144$, which simplifies to $r^2\cos\theta\sin\theta = 9$. Recognizing that $\cos\theta\sin\theta$ can be expressed as $\frac{1}{2}\sin(2\theta)$ is not directly needed here, but knowing $\cos\theta = \frac{1}{\sec\theta}$ and $\sin\theta = \frac{1}{\csc\theta}$ helps identify the correct form, which is $r^2 = 9\sec\theta\csc\theta$, matching choice A.

Which Answer Is a Polar Form of the Given Rectangular 16xy=14416 x y = 14416xy=144

Which Answer Is a Polar Form of the Given Rectangular $16 x y = 144$