Chapter 8, Problem 14RE

(a)

To determine

To calculate:

The given equation in the form of polar-co-ordinates:

  $xy=1$

Answer to Problem 14RE

The equation of the rectangular co-ordinates converts into a polar co-ordinates as $r=\frac{2}{\sqrt{\cos \theta \cdot \sin \theta }}$ .

Explanation of Solution

Given information:

  $xy=1$

Formula Used:

When a point is given with its rectangular co-ordinates $\left(x,y\right)$ , its polar co-ordinates $\left(r,\theta \right)$ are defined as:

  $\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

Calculation:

The given equation is:

  $xy=1$

Now need to convert the equation ofrectangular co-ordinates into polar co-ordinates as:

  $\begin{array}{l}xy=1\\ r\cos \theta \cdot r\sin \theta =1\\ r^2\left(\cos \theta \cdot \sin \theta \right)=4\\ r^2=\frac{4}{\cos \theta \cdot \sin \theta }\\ r=\frac{2}{\sqrt{\cos \theta \cdot \sin \theta }}\end{array}$

(b)

To determine

To graph:

The graph of the equation is need to drawn.

Explanation of Solution

Given information:

  $xy=1$

Graph:

  

Interpretation:

From the given data point:

The given equation is in the rectangular co-ordinates is drawn as above:

  $xy=1$