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avatar+818 

Find the coordinates of the center of the circle.
The points on the circle are (22,15), (-25,0), (22,-29).

 Mar 29, 2024
 #1
avatar+34 
+1

https://www.desmos.com/calculator/ecmqlf6gaz

 Mar 29, 2024
 #2
avatar+34 
+1
 Mar 29, 2024
 #3
avatar+128399 
+1

Using the square of the distances to equate R^2

 

(x - 22)^2 + (y - 15)^2  = (x -22)^2  + ( y + 29)^2

 

y^2 - 30y + 225  =  y^2 + 58y + 841

 

-30y - 58y  =  841  - 225

 

-88y = 616

 

y = -616 / 88  = -7

 

To find x

 

(x -22)^2 + (-7-15)^2  = (x + 25)^2 + ( -7 -0)^2

 

x^2 - 44x + 484 + 484  = x^2 + 50x + 625 + 49

 

-44x + 968 = 50x + 674

 

968 - 674 =  50x + 44x

 

294 = 94x

 

x = 294/94 =  147 / 47

 

Center  = ( 147/47 , -7)

 

cool cool cool

 Mar 29, 2024

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