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Q 15

Found in: Page 772


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Sketch the graphs of the equations

r=22+cosθ and localid="1649860998050" r=22+sinθ

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 12.

See the step by step solution

Step by Step Solution

Step 1. Given Information 

We have given the following two equations :-

r=22+cosθ and localid="1649861177655" r=22+sinθ

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=22+cosθ and r=22+sinθ

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=22+cosθ has x-axis as the major axis and the graph of r=22+sinθ 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 1r=a+ecosθ, where is the eccentricity.

The eccentricity of both ellipses is 12.

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