Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 9.6, Problem 21WE

(a)

To determine

To identify: the graph of the given quadratic equation

(a)

Expert Solution

Answer to Problem 21WE

The graph represents a parabola.

Explanation of Solution

Given: B=0

Calculation:

Substitute 1 for A , 0 for B , 2 for C , -8 for D , and 1 for E in the given equation.

x2+2x−8y+1=0

Graph the equation using any graphing utility.

Algebra and Trigonometry: Structure and Method, Book 2, Chapter 9.6, Problem 21WE , additional homework tip 1

Note that the graph represents a parabola.

Conclusion:

Therefore, the graph represents a parabola.

(b)

To determine

To identify: the graph of the given quadratic equation

(b)

Expert Solution

Answer to Problem 21WE

The graph represents a circle.

Explanation of Solution

Given: B=1

Calculation:

Substitute 1 for A , 0 for B , 2 for C , -8 for D , and 1 for E in the given equation.

x2+y2+2x−8y+1=0

Graph the equation using any graphing utility.

Algebra and Trigonometry: Structure and Method, Book 2, Chapter 9.6, Problem 21WE , additional homework tip 2

Note that the graph represents a circle.

Conclusion:

Therefore, the graph represents a circle.

(c)

To determine

To identify: the graph of the given quadratic equation

(c)

Expert Solution

Answer to Problem 21WE

The graph represents an ellipse.

Explanation of Solution

Given: B=4

Calculation:

Substitute 1 for A , 4 for B , 2 for C , -8 for D , and 1 for E in the given equation.

x2+4y2+2x−8y+1=0

Graph the equation using any graphing utility.

Algebra and Trigonometry: Structure and Method, Book 2, Chapter 9.6, Problem 21WE , additional homework tip 3

Note that the graph represents an ellipse.

Conclusion:

Therefore, the graph represents an ellipse.

(d)

To determine

To identify: the graph of the given quadratic equation

(d)

Expert Solution

Answer to Problem 21WE

The graph represents a hyperbola.

Explanation of Solution

Given: B=−4

Calculation:

Substitute 1 for A , - 4 for B , 2 for C , -8 for D , and 1 for E in the given equation.

x2−4y2+2x−8y+1=0

Graph the equation using any graphing utility.

Algebra and Trigonometry: Structure and Method, Book 2, Chapter 9.6, Problem 21WE , additional homework tip 4

Note that the graph represents a hyperbola.

Conclusion:

Therefore, the graph represents a hyperbola.

(e)

To determine

To find: the relationship between the coefficient A and B

(e)

Expert Solution

Answer to Problem 21WE

The relationship between the coefficients A and B gives a circle when A=B , a parabola when AB=0 , an ellipse when AB>0 , and a hyperbola when AB<0 .

Explanation of Solution

Calculation:

If the different equations are compared, here it is graphed with the general equation.

The relationship between the coefficients A and B gives a circle when A=B , a parabola when AB=0 , an ellipse when AB>0 , and a hyperbola when AB<0 .

Conclusion:

Therefore, the relationship between the coefficients A and B gives a circle when A=B , a parabola when AB=0 , an ellipse when AB>0 , and a hyperbola when AB<0 .

Chapter 9.6, Problem 20WE

Chapter 9.6, Problem 1ST

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

Ch. 9.1 - Prob. 11OE Ch. 9.1 - Prob. 12OE Ch. 9.1 - Prob. 13OE Ch. 9.1 - Prob. 14OE Ch. 9.1 - Prob. 15OE Ch. 9.1 - Prob. 1WE Ch. 9.1 - Prob. 2WE Ch. 9.1 - Prob. 3WE Ch. 9.1 - Prob. 4WE Ch. 9.1 - Prob. 5WE Ch. 9.1 - Prob. 6WE Ch. 9.1 - Prob. 7WE Ch. 9.1 - Prob. 8WE Ch. 9.1 - Prob. 9WE Ch. 9.1 - Prob. 10WE Ch. 9.1 - Prob. 11WE Ch. 9.1 - Prob. 12WE Ch. 9.1 - Prob. 13WE Ch. 9.1 - Prob. 14WE Ch. 9.1 - Prob. 15WE Ch. 9.1 - Prob. 16WE Ch. 9.1 - Prob. 17WE Ch. 9.1 - Prob. 18WE Ch. 9.1 - Prob. 19WE Ch. 9.1 - Prob. 20WE Ch. 9.1 - Prob. 21WE Ch. 9.1 - Prob. 22WE Ch. 9.1 - Prob. 23WE Ch. 9.1 - Prob. 24WE Ch. 9.1 - Prob. 25WE Ch. 9.1 - Prob. 26WE Ch. 9.1 - Prob. 27WE Ch. 9.1 - Prob. 28WE Ch. 9.1 - Prob. 29WE Ch. 9.1 - Prob. 30WE Ch. 9.1 - Prob. 31WE Ch. 9.1 - Prob. 32WE Ch. 9.1 - Prob. 1P Ch. 9.1 - Prob. 2P Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P Ch. 9.1 - Prob. 5P Ch. 9.1 - Prob. 6P Ch. 9.1 - Prob. 7P Ch. 9.1 - Prob. 8P Ch. 9.1 - Prob. 9P Ch. 9.1 - Prob. 10P Ch. 9.1 - Prob. 11P Ch. 9.1 - Prob. 12P Ch. 9.1 - Prob. 13P Ch. 9.1 - Prob. 14P Ch. 9.1 - Prob. 1MRE Ch. 9.1 - Prob. 2MRE Ch. 9.1 - Prob. 3MRE Ch. 9.1 - Prob. 4MRE Ch. 9.1 - Prob. 5MRE Ch. 9.1 - Prob. 6MRE Ch. 9.1 - Prob. 1CE Ch. 9.1 - Prob. 2CE Ch. 9.1 - Prob. 3CE Ch. 9.1 - Prob. 4CE Ch. 9.2 - Prob. 1OE Ch. 9.2 - Prob. 2OE Ch. 9.2 - Prob. 3OE Ch. 9.2 - Prob. 4OE Ch. 9.2 - Prob. 5OE Ch. 9.2 - Prob. 6OE Ch. 9.2 - Prob. 7OE Ch. 9.2 - Prob. 8OE Ch. 9.2 - Prob. 9OE Ch. 9.2 - Prob. 10OE Ch. 9.2 - Prob. 11OE Ch. 9.2 - Prob. 12OE Ch. 9.2 - Prob. 13OE Ch. 9.2 - Prob. 14OE Ch. 9.2 - Prob. 15OE Ch. 9.2 - Prob. 1WE Ch. 9.2 - Prob. 2WE Ch. 9.2 - Prob. 3WE Ch. 9.2 - Prob. 4WE Ch. 9.2 - Prob. 5WE Ch. 9.2 - Prob. 6WE Ch. 9.2 - Prob. 7WE Ch. 9.2 - Prob. 8WE Ch. 9.2 - Prob. 9WE Ch. 9.2 - Prob. 10WE Ch. 9.2 - Prob. 11WE Ch. 9.2 - Prob. 12WE Ch. 9.2 - Prob. 13WE Ch. 9.2 - Prob. 14WE Ch. 9.2 - Prob. 15WE Ch. 9.2 - Prob. 16WE Ch. 9.2 - Prob. 17WE Ch. 9.2 - Prob. 18WE Ch. 9.2 - Prob. 19WE Ch. 9.2 - Prob. 20WE Ch. 9.2 - Prob. 21WE Ch. 9.2 - Prob. 22WE Ch. 9.2 - Prob. 23WE Ch. 9.2 - Prob. 24WE Ch. 9.2 - Prob. 25WE Ch. 9.2 - Prob. 26WE Ch. 9.2 - Prob. 27WE Ch. 9.2 - Prob. 28WE Ch. 9.2 - Prob. 29WE Ch. 9.2 - Prob. 30WE Ch. 9.2 - Prob. 31WE Ch. 9.2 - Prob. 32WE Ch. 9.2 - Prob. 33WE Ch. 9.2 - Prob. 34WE Ch. 9.2 - Prob. 35WE Ch. 9.2 - Prob. 36WE Ch. 9.2 - Prob. 37WE Ch. 9.2 - Prob. 38WE Ch. 9.2 - Prob. 39WE Ch. 9.2 - Prob. 40WE Ch. 9.2 - Prob. 41WE Ch. 9.2 - Prob. 42WE Ch. 9.2 - Prob. 43WE Ch. 9.2 - Prob. 44WE Ch. 9.2 - Prob. 45WE Ch. 9.2 - Prob. 46WE Ch. 9.2 - Prob. 47WE Ch. 9.2 - Prob. 48WE Ch. 9.2 - Prob. 49WE Ch. 9.2 - Prob. 50WE Ch. 9.3 - Prob. 1OE Ch. 9.3 - Prob. 2OE Ch. 9.3 - Prob. 3OE Ch. 9.3 - Prob. 4OE Ch. 9.3 - Prob. 5OE Ch. 9.3 - Prob. 6OE Ch. 9.3 - Prob. 7OE Ch. 9.3 - Prob. 8OE Ch. 9.3 - Prob. 9OE Ch. 9.3 - Prob. 10OE Ch. 9.3 - Prob. 11OE Ch. 9.3 - Prob. 12OE Ch. 9.3 - Prob. 1WE Ch. 9.3 - Prob. 2WE Ch. 9.3 - Prob. 3WE Ch. 9.3 - Prob. 4WE Ch. 9.3 - Prob. 5WE Ch. 9.3 - Prob. 6WE Ch. 9.3 - Prob. 7WE Ch. 9.3 - Prob. 8WE Ch. 9.3 - Prob. 9WE Ch. 9.3 - Prob. 10WE Ch. 9.3 - Prob. 11WE Ch. 9.3 - Prob. 12WE Ch. 9.3 - Prob. 13WE Ch. 9.3 - Prob. 14WE Ch. 9.3 - Prob. 15WE Ch. 9.3 - Prob. 16WE Ch. 9.3 - Prob. 17WE Ch. 9.3 - Prob. 18WE Ch. 9.3 - Prob. 19WE Ch. 9.3 - Prob. 20WE Ch. 9.3 - Prob. 21WE Ch. 9.3 - Prob. 22WE Ch. 9.3 - Prob. 23WE Ch. 9.3 - Prob. 24WE Ch. 9.3 - Prob. 25WE Ch. 9.3 - Prob. 26WE Ch. 9.3 - Prob. 27WE Ch. 9.3 - Prob. 28WE Ch. 9.3 - Prob. 29WE Ch. 9.3 - Prob. 30WE Ch. 9.3 - Prob. 31WE Ch. 9.3 - Prob. 32WE Ch. 9.3 - Prob. 33WE Ch. 9.3 - Prob. 34WE Ch. 9.3 - Prob. 35WE Ch. 9.3 - Prob. 36WE Ch. 9.3 - Prob. 37WE Ch. 9.3 - Prob. 38WE Ch. 9.3 - Prob. 1MRE Ch. 9.3 - Prob. 2MRE Ch. 9.3 - Prob. 3MRE Ch. 9.3 - Prob. 4MRE Ch. 9.3 - Prob. 5MRE Ch. 9.3 - Prob. 6MRE Ch. 9.3 - Prob. 1ST Ch. 9.3 - Prob. 2ST Ch. 9.3 - Prob. 3ST Ch. 9.3 - Prob. 4ST Ch. 9.3 - Prob. 5ST Ch. 9.3 - Prob. 6ST Ch. 9.3 - Prob. 7ST Ch. 9.3 - Prob. 8ST Ch. 9.4 - Prob. 1OE Ch. 9.4 - Prob. 2OE Ch. 9.4 - Prob. 3OE Ch. 9.4 - Prob. 4OE Ch. 9.4 - Prob. 5OE Ch. 9.4 - Prob. 6OE Ch. 9.4 - Prob. 1WE Ch. 9.4 - Prob. 2WE Ch. 9.4 - Prob. 3WE Ch. 9.4 - Prob. 4WE Ch. 9.4 - Prob. 5WE Ch. 9.4 - Prob. 6WE Ch. 9.4 - Prob. 7WE Ch. 9.4 - Prob. 8WE Ch. 9.4 - Prob. 9WE Ch. 9.4 - Prob. 10WE Ch. 9.4 - Prob. 11WE Ch. 9.4 - Prob. 12WE Ch. 9.4 - Prob. 13WE Ch. 9.4 - Prob. 14WE Ch. 9.4 - Prob. 15WE Ch. 9.4 - Prob. 16WE Ch. 9.4 - Prob. 17WE Ch. 9.4 - Prob. 18WE Ch. 9.4 - Prob. 19WE Ch. 9.4 - Prob. 20WE Ch. 9.4 - Prob. 21WE Ch. 9.4 - Prob. 22WE Ch. 9.4 - Prob. 23WE Ch. 9.4 - Prob. 24WE Ch. 9.4 - Prob. 25WE Ch. 9.4 - Prob. 26WE Ch. 9.4 - Prob. 27WE Ch. 9.4 - Prob. 28WE Ch. 9.4 - Prob. 29WE Ch. 9.4 - Prob. 30WE Ch. 9.4 - Prob. 31WE Ch. 9.4 - Prob. 32WE Ch. 9.4 - Prob. 33WE Ch. 9.4 - Prob. 34WE Ch. 9.4 - Prob. 35WE Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.5 - Prob. 1OE Ch. 9.5 - Prob. 2OE Ch. 9.5 - Prob. 3OE Ch. 9.5 - Prob. 4OE Ch. 9.5 - Prob. 5OE Ch. 9.5 - Prob. 6OE Ch. 9.5 - Prob. 7OE Ch. 9.5 - Prob. 8OE Ch. 9.5 - Prob. 9OE Ch. 9.5 - Prob. 1WE Ch. 9.5 - Prob. 2WE Ch. 9.5 - Prob. 3WE Ch. 9.5 - Prob. 4WE Ch. 9.5 - Prob. 5WE Ch. 9.5 - Prob. 6WE Ch. 9.5 - Prob. 7WE Ch. 9.5 - Prob. 8WE Ch. 9.5 - Prob. 9WE Ch. 9.5 - Prob. 10WE Ch. 9.5 - Prob. 11WE Ch. 9.5 - Prob. 12WE Ch. 9.5 - Prob. 13WE Ch. 9.5 - Prob. 14WE Ch. 9.5 - Prob. 15WE Ch. 9.5 - Prob. 16WE Ch. 9.5 - Prob. 17WE Ch. 9.5 - Prob. 18WE Ch. 9.5 - Prob. 19WE Ch. 9.5 - Prob. 20WE Ch. 9.5 - Prob. 21WE Ch. 9.5 - Prob. 22WE Ch. 9.5 - Prob. 23WE Ch. 9.5 - Prob. 24WE Ch. 9.5 - Prob. 25WE Ch. 9.5 - Prob. 26WE Ch. 9.5 - Prob. 27WE Ch. 9.5 - Prob. 28WE Ch. 9.5 - Prob. 29WE Ch. 9.5 - Prob. 30WE Ch. 9.5 - Prob. 31WE Ch. 9.5 - Prob. 32WE Ch. 9.5 - Prob. 33WE Ch. 9.5 - Prob. 34WE Ch. 9.5 - Prob. 35WE Ch. 9.5 - Prob. 1MRE Ch. 9.5 - Prob. 2MRE Ch. 9.5 - Prob. 3MRE Ch. 9.5 - Prob. 4MRE Ch. 9.5 - Prob. 5MRE Ch. 9.5 - Prob. 6MRE Ch. 9.5 - Prob. 7MRE Ch. 9.5 - Prob. 8MRE Ch. 9.5 - Prob. 9MRE Ch. 9.5 - Prob. 10MRE Ch. 9.6 - Prob. 1OE Ch. 9.6 - Prob. 2OE Ch. 9.6 - Prob. 3OE Ch. 9.6 - Prob. 4OE Ch. 9.6 - Prob. 5OE Ch. 9.6 - Prob. 6OE Ch. 9.6 - Prob. 7OE Ch. 9.6 - Prob. 8OE Ch. 9.6 - Prob. 9OE Ch. 9.6 - Prob. 10OE Ch. 9.6 - Prob. 11OE Ch. 9.6 - Prob. 12OE Ch. 9.6 - Prob. 13OE Ch. 9.6 - Prob. 14OE Ch. 9.6 - Prob. 1WE Ch. 9.6 - Prob. 2WE Ch. 9.6 - Prob. 3WE Ch. 9.6 - Prob. 4WE Ch. 9.6 - Prob. 5WE Ch. 9.6 - Prob. 6WE Ch. 9.6 - Prob. 7WE Ch. 9.6 - Prob. 8WE Ch. 9.6 - Prob. 9WE Ch. 9.6 - Prob. 10WE Ch. 9.6 - Prob. 11WE Ch. 9.6 - Prob. 12WE Ch. 9.6 - Prob. 13WE Ch. 9.6 - Prob. 14WE Ch. 9.6 - Prob. 15WE Ch. 9.6 - Prob. 16WE Ch. 9.6 - Prob. 17WE Ch. 9.6 - Prob. 18WE Ch. 9.6 - Prob. 19WE Ch. 9.6 - Prob. 20WE Ch. 9.6 - Prob. 21WE Ch. 9.6 - Prob. 1ST Ch. 9.6 - Prob. 2ST Ch. 9.6 - Prob. 3ST Ch. 9.6 - Prob. 4ST Ch. 9.6 - Prob. 5ST Ch. 9.6 - Prob. 6ST Ch. 9.7 - Prob. 1OE Ch. 9.7 - Prob. 2OE Ch. 9.7 - Prob. 3OE Ch. 9.7 - Prob. 4OE Ch. 9.7 - Prob. 5OE Ch. 9.7 - Prob. 6OE Ch. 9.7 - Prob. 7OE Ch. 9.7 - Prob. 8OE Ch. 9.7 - Prob. 9OE Ch. 9.7 - Prob. 10OE Ch. 9.7 - Prob. 11OE Ch. 9.7 - Prob. 12OE Ch. 9.7 - 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