Concept explainers
Draw a graph of the ellipse using given properties.
Answer to Problem 1PS
The equation of the ellipse is
Explanation of Solution
Given:
The distance between two foci is
Calculation:
A ellipse is the set of all points in a plane such that, for each point on the ellipse, the sum of its distances from two fixed points is a constant.
From definition,
If
Now,
The distance between two foci
From question,
And
The equation of ellipse is
The standard form of a ellipse is
Rewrite the given equation.
Center of the ellipse
The distance from the center to a focus.
Vertex
Focus
Eccentricity
The graph of the curve is given below.
Hence the equation of the ellipse is
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