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The points (2,3) and (3,2) lie on a circle whose center is on the x-axis. What is the radius of the circle?

 Jun 21, 2021
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The center (h,0 ) is the same distance from each of the points    (h,0) because it is on the x axis then y = 0

  distance from point 1 to center h,0

      sqrt [ (h-2)^2 + ( 0-3)^2 ]

 

  distance from point 2 to center

      sqrt [ (h-3)^2 + ( 0-2)^2 ]                  Now you have two equations, two unknowns ...solve for h,k

 

 

sqrt [ (h-2)^2 + ( 0-3)^2 ]   =     sqrt [ (h-3)^2 + ( 0-2)^2 ] 

 

(h-2)^2 + (0-3)^2     =     (h-3)^2 + ( 0-2)^2    

h^2 -4h + 4      + 9      =   h^2 -6h+9     +  4 

-4h + 4           + 9              =  -6h + 9       + 4

2h     +13                      =     13

2h  = 0

h=0

 

So the center is 0,0        can you calculate the radius now?     Need more help?     (use distance formula from 0,0 to either of the points)

 Jun 21, 2021

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