(a) Answer An ellipse Explanation Given information: e = 1 2 Calculation: As the eccentricity is between 0 This indicates an ellipse. (b) To determine To identify: Conic section given its eccentricity e = 1 . Answer A parabola Explanation Given information: e = 1 Calculation: On a parabola, e will always be 1 because the distance from the directix to a point, will always be the same as the distance from the point to the focus. (c) To determine To identify: Conic section given its eccentricity e = 1.25 . Answer A hyperbola Explanation Given information: e = 1.25 Calculation: A hyperbola will always have a value for e greater than 1 because the distance from the directrix to a point on the graph is always more than the distance from the point to the focus. (d) To determine To identify: Conic section given its eccentricity e = 0 . Answer A circle Explanation Given information: e = 0 Calculation: Because on a circle, the foci are at the center, c = 0. Since e = c a , This will always produce an e = 0 .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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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 10.5, Problem 5CFU

(a)

To determine

To identify: Conic section given its eccentricity e=12 .

(a)

Expert Solution

Answer to Problem 5CFU

An ellipse

Explanation of Solution

Given information: e=12

Calculation:

As the eccentricity is between 0

This indicates an ellipse.

(b)

To determine

To identify: Conic section given its eccentricity e=1 .

(b)

Expert Solution

Answer to Problem 5CFU

A parabola

Explanation of Solution

Given information: e=1

Calculation:

On a parabola, e will always be 1 because the distance from the directix to a point, will always be the same as the distance from the point to the focus.

(c)

To determine

To identify: Conic section given its eccentricity e=1.25 .

(c)

Expert Solution

Answer to Problem 5CFU

A hyperbola

Explanation of Solution

Given information: e=1.25

Calculation:

A hyperbola will always have a value for e greater than 1 because the distance from the directrix to a point on the graph is always more than the distance from the point to the focus.

(d)

To determine

To identify: Conic section given its eccentricity e=0 .

(d)

Expert Solution

Answer to Problem 5CFU

A circle

Explanation of Solution

Given information: e=0

Calculation:

Because on a circle, the foci are at the center, c = 0.

Since e=ca,

This will always produce an e=0 .

Chapter 10.5, Problem 4CFU

Chapter 10.5, Problem 6CFU

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFU Ch. 10.1 - Prob. 2CFU Ch. 10.1 - Prob. 3CFU Ch. 10.1 - Prob. 4CFU Ch. 10.1 - Prob. 5CFU Ch. 10.1 - Prob. 6CFU Ch. 10.1 - Prob. 7CFU Ch. 10.1 - Prob. 8CFU Ch. 10.1 - Prob. 9CFU Ch. 10.1 - Prob. 10CFU

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