Chapter H.1, Problem 20E

To determine

To find:The polar equation for the curve

Answer to Problem 20E

The polar equation of the curve is $r^2=8\cos ec2\theta$

Explanation of Solution

Given: $xy=4$

Calculation:

GivenCartesian equation $xy=4$

We have $x=r\cos \theta$

  $y=r\sin \theta$

  $\Rightarrow r\cos \theta \cdot r\sin \theta =4$

  $\Rightarrow r^2=\frac{4}{\sin \theta \cos \theta }$

  $\Rightarrow r^2=\frac{8}{\sin 2\theta }$

  $\Rightarrow r^2=8\cos ec2\theta$

  $\therefore$ The polar equation of the curve is $r^2=8\cos ec2\theta$

Conclusion:

Therefore, the polar equation of the curve is $r^2=8\cos ec2\theta$