
Concept explainers
(a)
To graph the ellipses with given equations on same graph.
(a)

Explanation of Solution
Given:
The given equations of ellipses are
Calculation:
The following is the graph of both ellipses on single graph
(b)
To describe the difference between two graphs.
(b)

Explanation of Solution
Given:
The given equations of ellipses are -
Calculation:
One ellipse is much flatter than the other. Both have the same major axis, but one has a much shorter minor axis.
(c)
To find the eccentricity of each ellipse.
(c)

Answer to Problem 39PPS
Explanation of Solution
Given:
The given equations of ellipses are -
Calculation:
The eccentricity is calculated by the following formula-
Therefore, the eccentricity for first graph is
And the eccentricity for second graph is
(d)
To make the conjecture about the eccentricity and shape of each ellipse.
(d)

Explanation of Solution
Given:
The given equations of ellipses are -
Calculation:
As the eccentricity of an ellipse approaches zero, it approaches a
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