a.
To find: The eccentricity and identify the given conic.
a.
Answer to Problem 65RE
The eccentricity of the given polar equation of a conic is
Explanation of Solution
Given information:
The polar equation of the conic is
Concept used:
The general equation of a conic in the polar form is
Where
If
Calculation:
Given polar equation is
Converting the given polar equation to the general form as above by the suitable rearrangement.
The required polar equation represents general form is
Comparing with the general form find
Conclusion:
The eccentricity is obtained as
Therefore, the given polar equation represents a hyperbola.
b.
To sketch: The conic and label the vertex.
b.
Answer to Problem 65RE
From the graph it can be observed that the vertices of the conic is/are
Explanation of Solution
Given information:
Polar equation of the conic is
Graph:
Sketch the graph using graphing utility.
Step 1: Press WINDOW button to access the Window editor.
Step 2: Press
Step 3: Enter the expression
Step 4: Press GRAPH button to graph the function and adjust the windows according to the graph.
The graph is obtained as:
Interpretation:
From the above graph it can be observed that the vertices of the conic are
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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