Convert the rectangular equation to polar form. Assume
$a 0$
$x y = 10$
A) $r ^ { 2 } = 10 \sec 2 \theta$
B) $r ^ { 2 } = 20 \csc 2 \theta$
C) $r ^ { 2 } = 20 \sec 2 \theta$
D) $r ^ { 2 } = 10 \csc 2 \theta$
E) $r ^ { 2 } = 20 \cos 2 \theta$

Question

Convert the rectangular equation to polar form. Assume 
$a > 0$ 
$x y = 10$ 
A) $r ^ { 2 } = 10 \sec 2 \theta$
B) $r ^ { 2 } = 20 \csc 2 \theta$
C) $r ^ { 2 } = 20 \sec 2 \theta$
D) $r ^ { 2 } = 10 \csc 2 \theta$
E) $r ^ { 2 } = 20 \cos 2 \theta$

Quizplus · Accepted Answer

The rectangular equation $xy = 10$ can be converted to polar form using the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation gives $r\cos\theta \cdot r\sin\theta = 10$, which simplifies to $r^2\cos\theta\sin\theta = 10$. Using the double angle identity $\sin(2\theta) = 2\sin\theta\cos\theta$, we can rewrite the equation as $r^2(2\sin\theta\cos\theta) = 20$, or $r^2 = \frac{20}{\sin(2\theta)}$, which is equivalent to $r^2 = 20\csc(2\theta)$.

Convert the Rectangular Equation to Polar Form a>0a > 0a>0 xy=10x y = 10xy=10

Convert the Rectangular Equation to Polar Form $a > 0$ $x y = 10$