Chapter 11.3, Problem 70E

(a)

To determine

To graph: The curve $r$ for $k=1,3,5,7,9$ .

Answer to Problem 70E

The curves are hyperbolas.

Explanation of Solution

Given information:

The curve: $r=\frac{k}{1+\cos \theta }$

Calculation:

The given curve is $r=\frac{k}{1+\cos \theta }$ .

For values of $k=1,3,5,7,9$ ; the graph of the given curve is shown below:

  

From the above graphs it is seen that the curves are parabolas.

(b)

To determine

To determine: The conjecture about the graphs for $k>0$ and $k\to 0^{+}$ .

Answer to Problem 70E

The limit of the graph is the negative x -axis.

Explanation of Solution

Given information:

The curve: $r=\frac{k}{1+\cos \theta }$

Calculation:

The given curve is $r=\frac{k}{1+\cos \theta }$ .

For values of $k=1,3,5,7,9$ ; the graph of the given curve is shown below:

  

From the above graphs it is seen that the curves are parabolas.

As $k\to 0^{+}$ , the limit of the graph is the negative x -axis.