Convert the rectangular equation to polar form. Assume $a 0$ $x y = 17$
A) $r ^ { 2 } = 17 \sec 2 \theta$
B) $r ^ { 2 } = 34 \csc 2 \theta$
C) $r ^ { 2 } = 34 \cos 2 \theta$
D) $r ^ { 2 } = 17 \csc 2 \theta$
E) $r ^ { 2 } = 34 \sec 2 \theta$

Question

Convert the rectangular equation to polar form. Assume $a > 0$ $x y = 17$ 
A) $r ^ { 2 } = 17 \sec 2 \theta$
B) $r ^ { 2 } = 34 \csc 2 \theta$
C) $r ^ { 2 } = 34 \cos 2 \theta$
D) $r ^ { 2 } = 17 \csc 2 \theta$
E) $r ^ { 2 } = 34 \sec 2 \theta$

Quizplus · Accepted Answer

To convert the rectangular equation $xy = 17$ to polar form, use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the equation gives $r\cos\theta \cdot r\sin\theta = 17$, which simplifies to $r^2\cos\theta\sin\theta = 17$. Multiplying both sides by 2 for a common identity, $2r^2\cos\theta\sin\theta = 34$, which can be rewritten using the double angle identity $\sin(2\theta) = 2\sin\theta\cos\theta$ as $r^2\sin(2\theta) = 34$. Rearranging gives $r^2 = 34 \csc(2\theta)$, matching choice B.

Convert the Rectangular Equation to Polar Form a>0a > 0a>0 xy=17x y = 17xy=17

Convert the Rectangular Equation to Polar Form $a > 0$ $x y = 17$