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

 Jun 4, 2024
 #1
avatar+129401 
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Using the square of the distance formula = r^2....let the center = (x,y)

So we have

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

 

(y -15)^2  = (  y - 29)^2

 

y^2 -30y + 225  =  y^2 -58y + 841

 

28y =  616

 

y = 616 / 28 =  22

 

So...using  (22,15)  and (-25,0)   we can  find x  as

 

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

 

(x -22)^2  + 49  = ( x + 25)^2  + 484

 

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

 

-44x  + 49  =  50x + 625

 

- 94x  =  576

 

x = 576 / -94 = -288/47

 

Coordinates are  ( -288/47 , 22)

 

 

cool cool cool

 Jun 4, 2024

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