Which answer is a polar form of the given rectangular equation?
$$25 x y = 225$$
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 rectangular equation $25xy = 225$ to polar form, use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation yields $25(r\cos\theta)(r\sin\theta) = 225$, which simplifies to $r^2\cos\theta\sin\theta = 9$. Recognizing that $\cos\theta\sin\theta$ can be expressed as $\sec\theta\csc\theta$ for non-zero values of $\theta$, the correct polar form is $r^2 = 9\sec\theta\csc\theta$.

Which Answer Is a Polar Form of the Given Rectangular 25xy=22525 x y = 22525xy=225

Which Answer Is a Polar Form of the Given Rectangular $25 x y = 225$