Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Question

Chapter 9.4, Problem 25WE

(a)

To determine

To find: the value of c .

(a)

Expert Solution

Answer to Problem 25WE

The value of c is 0 .

Explanation of Solution

Given:

Suppose that a=b in the equation x2a2+y2b2=1 .

Calculation:

Use the relation c2=a2−b2 to find the value of c .

It is given that a=b . Substitute b for a in the relation.

c2=b2−b2=0c=0

Conclusion:

Therefore, the value of c is 0 .

(b)

To determine

To find: the value of e .

(b)

Expert Solution

Answer to Problem 25WE

The value of e is 0.

Explanation of Solution

Given:

Calculation:

The eccentricity e is defined by e=ca .

Substitute 0 for c in e .

e=0a=0

Conclusion:

Therefore, the value of e is 0.

(c)

To determine

To find: the position of two foci.

(c)

Expert Solution

Answer to Problem 25WE

Therefore, the foci are at the centre.

Explanation of Solution

Given:

Calculation:

The distance of the foci from the centre is given by c .

Since the value of c is 0, the distance of the foci from the center is 0.

Therefore, the foci are at the centre.

Conclusion:

Therefore, the foci are at the centre.

(d)

To determine

To find: the special ellipse will be the graph.

(d)

Expert Solution

Answer to Problem 25WE

Therefore, the given ellipse is a circle

Explanation of Solution

Given:

Calculation:

The foci of the given ellipse are at the centre.

The sum of the distances from any point on the ellipse to the foci is constant.

Since the two foci of the given ellipse are at the same point and at the center, the distances to all points on the ellipse from the center are equal, which makes it a circle.

Conclusion:

Therefore, the given ellipse is a circle

Chapter 9.4, Problem 24WE

Chapter 9.4, Problem 26WE

Chapter 9 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 9.1 - Prob. 1OE Ch. 9.1 - Prob. 2OE Ch. 9.1 - Prob. 3OE Ch. 9.1 - Prob. 4OE Ch. 9.1 - Prob. 5OE Ch. 9.1 - Prob. 6OE Ch. 9.1 - Prob. 7OE Ch. 9.1 - Prob. 8OE Ch. 9.1 - Prob. 9OE Ch. 9.1 - Prob. 10OE

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