Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
Question
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Chapter 7, Problem 47RE
To determine

Find the equation of the circle.

Expert Solution & Answer
Check Mark

Answer to Problem 47RE

  x2+y2−4x+4y−1=0

Graph is verified.

Explanation of Solution

Given information:

Find the equation of the circle.

  x2+y2+Dx+Ey+F=0

That passes through the points. Verify your result using a graphing utility.

  Precalculus with Limits, Chapter 7, Problem 47RE , additional homework tip 1

Calculation:

Consider the given equation and graph,

  x2+y2+Dx+Ey+F=0

  Precalculus with Limits, Chapter 7, Problem 47RE , additional homework tip 2

Circle passes through these points (2,1)(5,−2),(−1,−2) it is given

Circle passes through the points (2,1)

  x2+y2+Dx+Ey+F=022+12+D×2+E×1+F=04+1+2D+E+F=02D+E+F=−5........(1)

Similarly circle passes through the points (5,−2),(−1,−2)

  x2+y2+Dx+Ey+F=0−12+−22+D×−1+E×−2+F=0−D−2E+F=−5........(2)

  x2+y2+Dx+Ey+F=052+−22+D×5+E×−2+F=05D−2E+F=−29........(3)

Multiply equation (2) with 2 and add to equation (1)

  2D+E+F=−5−2D−4E+2F=−10−3E+3F=−15orE−F=5

Multiply equation (3) with 2 and equation (1) with 5 and add them.

  −10D−5E−5F=2510D−4E+2F=−58−9E−3F=−33or3E+F=11

Multiply equation (2) with 3 and add to equation 3E+F=11

  −3E+3F=−153E+F=114F=−4F=−1

Substitute F=−1 in equation E−F=5

  E−F=5E=5−1E=4

Put value of E=4 and F=−1 equation (1)

  2D+E+F=−52D+4−1=−52D=−8D=−4

Now substitute all calculated values in equation x2+y2+Dx+Ey+F=0

  x2+y2−4x+4y−1=0

The graph is shown as.

  Precalculus with Limits, Chapter 7, Problem 47RE , additional homework tip 3

The points lie on the circle hence verified.

Hence, the equation of circle is x2+y2−4x+4y−1=0

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Chapter 7, Problem 46RE
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Chapter 7, Problem 48RE

Chapter 7 Solutions

Precalculus with Limits

Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
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