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avatar+2729 

Find the coordinates of the center of the circle.

 

 Jan 15, 2025
 #1
avatar+130317 
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We need to solve these equations equating radii

 

x^2 + y^2  = ( x + 3)^2 + (y -2)^2

 

x^2 + y^2  =  x^2 + 6x + 9  + y^2 - 4y + 4

 

4y - 6x  =  13      (1)

 

And

 

x^2 + y^2   = (x + 2)^2  + (y -1)^2

 

x^2 + y^2 = x^2 + 4x + 4 + y^2 -2y + 1

 

2y - 4x  = 5    multiply this through by -2  →   -4y + 8x = -10     ( 2)

 

Add (1) , (2)

 

2x  =  3

x  = 3/2

 

And 

2y - 4(3/2)  = 5

2y - 6  = 5

2y = 11

y = 11/2

 

Center  =  ( 3/2 , 11/2)

 

cool cool cool

 Jan 15, 2025

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