EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
Question
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Chapter 7, Problem 47RE
To determine

To Find: the equation of the circle x2+y2+Dx+Ey+F=0 that passes through the given points and plot the points and graph the circle.

Expert Solution & Answer
Check Mark

Answer to Problem 47RE

The equation of the circle is x2+y2−2x+2y−23=0

The graph is

  EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 47RE , additional homework tip 1

Explanation of Solution

Given information:

The equation of the circle is given as x2+y2+Dx+Ey+F=0 and it passes through the points (4,3),(−2,−5),(1,4) from the figure.

  EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 47RE , additional homework tip 2

Calculation:

First let us substitute a point in the given equation.

For (4,3) the equation becomes

  (4)2+(3)2+D(4)+E(3)+F=016+9+4D+3E+F=04D+3E+F+25=0     ⋯(i)

Let us substitute (−2,−5) get other equation.

  (−2)2+(−5)2+(−2)D+(−5)E+F=04+25−2D−5E+F=0−2D−5E+F+29=0    ⋯(ii)

Let us substitute (1,4)

  (1)2+(4)2+(1)D+(4)E+F=01+16+D+4E+F=0D+4E+F+17=0   ⋯(iii)

Now subtract equations (i) and (ii) , we get,

  4D+3E+F+25+2D+5E−F−29=06D+8E−4=03D+4E=2  ⋯(iv)

Now subtract equations (ii) and (iii) , we get

  −2D−5E+F+29−D−4E−F−17=0−3D−9E+12=0D+3E=4  ⋯(v)

Now to eliminate a term let us multiply equation (v) by (iii) and subtract with equation (iv)

The result is

  3D+4E−3(D+3E)=2−3(4)3D+4E−3D−9E=2−12−5E=−10E=2

Substitute E=2 in (v) to get other values.

  D+3E=4D+3(2)=4D=4−6D=−2

Put E=2 and D=−2 in (iii) , The value of F is

  D+4E+F+17=0−2+4(2)+F+17=0−2+8+F+17=0F=−23

Hence the equation of the circle is x2+y2−2x+2y−23=0

The graph is as follows.

  EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 47RE , additional homework tip 3

Conclusion:

The equation of the circle is x2+y2−2x+2y−23=0

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

Chapter 7 Solutions

EBK PRECALCULUS W/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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