• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q 15

Expert-verified Found in: Page 772 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Sketch the graphs of the equations$r=\frac{2}{2+\mathrm{cos}\theta }$ and localid="1649860998050" $r=\frac{2}{2+\mathrm{sin}\theta }$What is the relationship between these graphs? What is the eccentricity of each graph?

The graphs of the given equations are as following :- Both the graphs are ellipse with focus at origin. One has major axis x-axis and other has y-axis.

The eccentricity of both graphs is $\frac{1}{2}$.

See the step by step solution

## Step 1. Given Information

We have given the following two equations :-

$r=\frac{2}{2+\mathrm{cos}\theta }$ and localid="1649861177655" $r=\frac{2}{2+\mathrm{sin}\theta }$

We have to draw the graph of these equations. We have to find the relationship between the graphs. Also we have to find the eccentricity of each graph.

## Step 2. Draw graphs of the equations

The given two equations are :-

$r=\frac{2}{2+\mathrm{cos}\theta }$ and $r=\frac{2}{2+\mathrm{sin}\theta }$

We can draw the graph of these equations as following :- ## Step 3. Find relationship between the graphs :-

We draw the graphs of given equations as following :- We can see that both the graphs are ellipses. The graph of ellipse $r=\frac{2}{2+\mathrm{cos}\theta }$ has x-axis as the major axis and the graph of $r=\frac{2}{2+\mathrm{sin}\theta }$ has y-axis as the major x-axis. The focus of both ellipses at origin.

## Step 4. Eccentricity of graphs

From the graph we can see that the both equations are Ellipses.

Compare the given equations with the equation $\frac{1}{r}=a+e\mathrm{cos}\theta$, where is the eccentricity.

The eccentricity of both ellipses is $\frac{1}{2}$. ### Want to see more solutions like these? 