(a) Explanation Given information: The equation is x 2 + y 2 + A x + B y + C . The given points are ( − 1 , 12 ) , ( 5 , 10 ) , ( 9 , 2 ) Formula used: Solving a system of three linear equations in three variables: Step 1: Write each equation in the form of A x + B y + C z = D . This is the standard form. Step 2: Take a pair of equations and by the addition method, eliminate one of the variables. Step 3: Now, take a different pair of equations and eliminate the same variable. Step 4: The resulting system has two equations in two variables. Solve this system by using any method out of substitution or addition method. Step 5: Put the values of the variables found in step 4 into any of the three original equations that has the third variable. Find the third variable. Step 6: Verify your answer by substituting the solution set in the original equations. Calculation: Substitute ( − 1 , 12 ) in x 2 + y 2 + A x + B y + C . Substitute ( 5 , 10 ) in x 2 + y 2 + A x + B y + C . Substitute ( 9 , 2 ) in x 2 + y 2 + A x + B y + C . After substitution, Equation A in standard form is; − A + 12 B + C = − 145 …… {A} Equation B in standard form is; 5 A + 10 B + C = − 125 …… {B} Equation C in standard form is; 9 A + 2 B + C = − 85 …… {C} Multiply equation A by 5 as: − 5 A + 60 B + 5 C = − 725 …… {D} Multiply equation A by 9 as: − 9 A + 108 B + 9 C = − 1305 …… {E} Eliminate A from equation B and D as: − 5 A + 60 B + 5 C = − 725 5 A + 10 B + C = − 125 _ 70 B + 6 C = − 850 Hence the new equation is: 70 B + 6 C = − 850 …… {F} Eliminate A from equation E and C as: − 9 A + 108 B + 9 C = − 1305 9 A + 2 B + C = − 85 _ 110 B + 10 C = − 1390 11 B + C = − 139 Hence the new equation is: 11 B + C = − 139 …… {G} Multiply equation G by − 6 as: − 66 B − 6 C = 834 …… {H} Now solve the equation F and H as: (b) To determine To calculate: The radius and the center of the circle whose equation is of the form x 2 + y 2 + A x + B y + C and passes through the points, ( − 1 , 12 ) , ( 5 , 10 ) , ( 9 , 2 ) .

2nd Edition

ISBN: 9781260119459

Author: Miller

Publisher: MCG CUSTOM

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Chapter 5.2, Problem 66PE

(a)

To determine

To calculate: An equation of the form of x2+y2+Ax+By+C=0 that represents the circle that passes through the given points:

(−1,12),(5,10),(9,2)

(b)

To determine

To calculate: The radius and the center of the circle whose equation is of the form x2+y2+Ax+By+C and passes through the points, (−1,12),(5,10),(9,2).

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Chapter 5.2, Problem 65PE

Chapter 5.2, Problem 67PE

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Chapter 5 Solutions

ALEKS 360 COLLEGE ALGEBRA 18WK >I<

Knowledge Booster

An equation of the form of x 2 + y 2 + A x + B y + C = 0 that represents the circle that passes through the given points: ( − 1 , 12 ) , ( 5 , 10 ) , ( 9 , 2 )

Solution Summary: The author explains how to solve a system of three linear equations in three variables.

To calculate: An equation of the form of x2+y2+Ax+By+C=0 that represents the circle that passes through the given points:

(−1,12),(5,10),(9,2)

To calculate: The radius and the center of the circle whose equation is of the form x2+y2+Ax+By+C and passes through the points, (−1,12),(5,10),(9,2).

Want to see the full answer?

Chapter 5 Solutions

An equation of the form of x 2 + y 2 + A x + B y + C = 0 that represents the circle that passes through the given points: ( − 1 , 12 ) , ( 5 , 10 ) , ( 9 , 2 )

Solution Summary: The author explains how to solve a system of three linear equations in three variables.

To calculate: An equation of the form of x2+y2+Ax+By+C=0 that represents the circle that passes through the given points: (−1,12),(5,10),(9,2)

To calculate: The radius and the center of the circle whose equation is of the form x2+y2+Ax+By+C and passes through the points, (−1,12),(5,10),(9,2).

Want to see the full answer?

Chapter 5 Solutions

To calculate: An equation of the form of x2+y2+Ax+By+C=0 that represents the circle that passes through the given points:

(−1,12),(5,10),(9,2)