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Find the center of the circle below.

 

 Dec 29, 2023
 #1
avatar+129487 
+1

Let (x,y)  be the center

 

Since all radiuses are equal  the distance from the center to any of the  points  is equal

 

So  we can solve this  using (-7,10) and (5,4)

 

(x + 7)^2  + ( y -10)^2  =  (x - 5)^2  + ( y - 4)^2        simplify

 

x^2 + 14x + 49 + y^2 - 20y + 100  = x^2 -10x + 25 + y^2 -8y + 16

 

24x  - 12y  =  -108    ⇒     2x - y  = - 9   ⇒  y= 2x + 9      (1) 

 

And using  (-7,10) and (15, -10)

 

(x + 7)^2  + (y-10)^2  = (x -15)^2 + ( y +10)^2

 

x^2 + 14x + 49 + y^2 - 20y + 100  = x^2 -30x + 225 + y^2 + 20y + 100

 

44x - 40y  = 176

 

11x - 10y = 44       (2)

 

Sub (1)  into (2)

 

11x - 10 ( 2x + 9) =  44

 

11x -20x - 90  = 44

 

-9x = 134

 

x= -134/9

 

y = 2(-134/9) + 9  =  -187/9

 

 

cool cool cool

 Dec 29, 2023

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