(a) Answer ( x − k ) 2 + ( y − k ) 2 = 4 Explanation Given information: Critical Thinking: Consider a family of circles in which h = k and the radius is 2. Let k be any real number. Calculation: ( x − h ) 2 + ( y − k ) 2 = r 2 If h = k and r = 2 , then ( x − k ) 2 + ( y − k ) 2 = 4 (b) To determine To graph: Three members of this family on the same set of axes. Answer The graph Explanation Given information: Critical Thinking: Consider a family of circles in which h = k and the radius is 2. Let k be any real number. Calculation: Graphs are: x 2 + y 2 = 4 ( x − 1 ) 2 + ( y − 1 ) 2 = 4 ( x − 2 ) 2 + ( y − 2 ) 2 = 4 (c) To determine To write: A description of all members of this family of circles. Answer If h = k and k is any real number, then the circles will be such that the center always falls along the line y = x . Explanation Given information: Critical Thinking: Consider a family of circles in which h = k and the radius is 2. Let k be any real number. Calculation: If h = k and k is any real number, then The circles will be such that the center always falls along the line y = x .

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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Videos

Question

Chapter 10.2, Problem 45E

(a)

To determine

To write: The equation of the family of circles.

(a)

Expert Solution

Answer to Problem 45E

(x−k)2+(y−k)2=4

Explanation of Solution

Given information: Critical Thinking: Consider a family of circles in which h = k and the radius is 2. Let k be any real number.

Calculation:

(x−h)2+(y−k)2=r2

If h=k and r=2, then

(x−k)2+(y−k)2=4

(b)

To determine

To graph: Three members of this family on the same set of axes.

(b)

Expert Solution

Answer to Problem 45E

The graph

Explanation of Solution

Given information: Critical Thinking: Consider a family of circles in which h = k and the radius is 2. Let k be any real number.

Calculation:

Graphs are:

x2+y2=4(x−1)2+(y−1)2=4(x−2)2+(y−2)2=4

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.2, Problem 45E , additional homework tip 1

(c)

To determine

To write: A description of all members of this family of circles.

(c)

Expert Solution

Answer to Problem 45E

If h=k and k is any real number, then the circles will be such that the center always falls along the line y=x .

Explanation of Solution

Given information: Critical Thinking: Consider a family of circles in which h = k and the radius is 2. Let k be any real number.

Calculation:

If h=k and k is any real number, then

The circles will be such that the center always falls along the line y=x .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.2, Problem 45E , additional homework tip 2

Chapter 10.2, Problem 44E

Chapter 10.2, Problem 46E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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