Concept explainers
In Exercises 1-8, graph each ellipse and locate the foci.
To graph: The equation of ellipse
Explanation of Solution
Given information:
The ellipse equation:
Graph:
Let us consider the following ellipse equation:
And the general equation of the ellipse is as given below:
And comparing equations (I) and (II) to obtain:
And the equation is the general ellipse’s equation with
Since, the denominator of the
Simplifying
And
And for a standard ellipse equation, the vertices of an ellipse are
So, the vertices of the ellipse are
And the foci
Put the values of
The foci
Then, plot the endpoints and the foci and trace them to obtain a smooth curve as shown below:
Interpretation:
Thus, the foci of the provided ellipse equation are
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Chapter 9 Solutions
Precalculus (6th Edition)
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