Chapter 9.1, Problem 71AYU

To determine

To find: Equation using polar coordinates $\left(r,\theta \right)$.The Letters $x$ and $y$ represent rectangular coordinates.

Answer to Problem 71AYU

Solution:

$r^2\text{sin}2\theta =1$

Explanation of Solution

Given:

$2xy=1$

Calculation:

Use the formula,

$x=r\text{cos}\theta$ $y=r\text{sin}\theta$

We have,

$2xy=1$

$2*r\text{cos}\theta *r\text{sin}\theta =1$

$2r^2\text{cos}\theta \text{sin}\theta =1$

Using $2\text{cos}\theta \text{sin}\theta =\text{ sin}2\theta$,we have

$r^2\text{sin}2\theta =1$