Which answer is a polar form of the given rectangular equation?
$$9 x y = 144$$
A) $r ^ { 2 } = 16 \sec \theta \csc \theta$
B) $r ^ { 2 } = 4 \sec \theta \csc \theta$
C) $r ^ { 2 } = 4 \sin \theta \cos \theta$
D) $r ^ { 2 } = 16 \sin \theta \cos \theta$
E) $\theta = 16 \sin \theta \cos \theta$

Question

Quizplus · Accepted Answer

To convert the rectangular equation $9xy = 144$ to polar form, use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation yields $9(r\cos\theta)(r\sin\theta) = 144$, which simplifies to $r^2\cos\theta\sin\theta = 16$. Recognizing that $\sec\theta = \frac{1}{\cos\theta}$ and $\csc\theta = \frac{1}{\sin\theta}$, the equation can be rewritten as $r^2 = 16\sec\theta\csc\theta$, matching choice A.

Which Answer Is a Polar Form of the Given Rectangular 9xy=1449 x y = 1449xy=144

Which Answer Is a Polar Form of the Given Rectangular $9 x y = 144$