Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
2. Ellipses
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Exercise 1 Page 653

We are asked to complete the following sentence.

An is the set of all points (x,y) in a plane, the sum of whose distances from two distinct fixed points called is constant.

To do this, let's consider two distinct points in a plane and the set of all points (x,y), the sum of whose distances from the two points is constant.

ellipse

This curve is an example of an ellipse. An ellipse is defined as the set of all points in a plane such that the sum of the distances from two fixed points is constant. These two points are called the foci of the ellipse.

We can now complete the sentence.

An ellipse is the set of all points (x,y) in a plane, the sum of whose distances from two distinct fixed points called foci is constant.