Concept explainers
(a)
To find: The standard form ellipse for the given equation
(a)
Answer to Problem 41E
The standard form of the equation of ellipse
Explanation of Solution
Given information:
The equation of the ellipse is
Calculation:
Rewrite the given equation of ellipse.
Further simplify,
Simplify further,
Therefore, the standard form of the equation of ellipse
(b)
To find: The center, vertices, foci and eccentricity of the ellipse
(b)
Answer to Problem 41E
The center, vertices, foci and eccentricity of the ellipse
Explanation of Solution
Given information:
The equation of the ellipse is
Calculation:
As calculated in part(a) the standard form of the equation of ellipse is
Compare the equation of ellipse
This gives
Use the formula.
Use the formula for eccentricity.
The center of the ellipse is
The vertices of the ellipse are:
The foci of the ellipse are:
The eccentricity of ellipse is
Therefore, The center, vertices, foci and eccentricity of the ellipse
(c)
To graph: The ellipse of equation
(c)
Answer to Problem 41E
The graph of the ellipse
Explanation of Solution
Given information:
The equation of the ellipse is
Calculation:
The graph of the ellipse
Figure (1)
The graph of the equation
Figure (2)
As both the graphs gives the same values at each point.
Therefore, both the graphs are similar.
Chapter 9 Solutions
Precalculus with Limits: A Graphing Approach
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