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Find the coordinates of the center of the circle.

 

 Jan 13, 2024

Best Answer 

 #1
avatar+36919 
+1

Using distance formula, the distance^2 from a,b to each of the points on the circle is the same ....

    to 2,0 and 7,1 :

           (a-2)^2 + (b-0)^2  = (a-7)^2 + (b-1)^2       simplify to 

10a+2b = 46

 

    to  2,0 and 3,5 

           ( a-2)^2  + ( b-0)^2  = (a-3)^2 + (b-5)^2    simplify to 

2a +10b = 30 

    Now you have two equations relating two unknowns....solve for a and b 

Multiply top equation by -5 to get 

-50a - 10 b = -230    and add it to the second equation to get 

-48a = -200 

a = 4.167.      use this value of 'a' in one of the equatins to find  b = 2.167           

 Jan 13, 2024
edited by ElectricPavlov  Jan 13, 2024
 #1
avatar+36919 
+1
Best Answer

Using distance formula, the distance^2 from a,b to each of the points on the circle is the same ....

    to 2,0 and 7,1 :

           (a-2)^2 + (b-0)^2  = (a-7)^2 + (b-1)^2       simplify to 

10a+2b = 46

 

    to  2,0 and 3,5 

           ( a-2)^2  + ( b-0)^2  = (a-3)^2 + (b-5)^2    simplify to 

2a +10b = 30 

    Now you have two equations relating two unknowns....solve for a and b 

Multiply top equation by -5 to get 

-50a - 10 b = -230    and add it to the second equation to get 

-48a = -200 

a = 4.167.      use this value of 'a' in one of the equatins to find  b = 2.167           

ElectricPavlov Jan 13, 2024
edited by ElectricPavlov  Jan 13, 2024

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