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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).

 Mar 15, 2024
 #1
avatar+44 
+2

Are you familiar with the distance formula? \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

You can plug in \(x_2\) as 22 and \(x_1\) as \(x\), and the corresponding values for y (15 or -29 and y) and make three equations

(for context, (x, y) is the center of the circle). Then, you solve the system!

 

If you have any questions, please contact!

-webcalcman

 Mar 15, 2024
 #2
avatar+128794 
+2

Using the square of the  distance  formula, equate r^2

 

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

 

(y -15)^2  = (y +29)^2

 

y^2 -30y + 225   =  y^2  + 58y + 841

 

-88y  =  616

 

y  = -616/88  =   -7

 

So....using this again

 

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

 

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

 

-44x  + 968  =   50x + 674

 

-94x  = -294

 

x =  294/94 = 147/47

 

The center is ( 147 / 47 , -7)

 

 

cool cool cool

 Mar 15, 2024

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