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

 May 31, 2021
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If  the  center  lies  on the  x axis,  then  let the  center =  (x, 0)

 

And using the  square  of the distance formula.....the distance  rom the  center to both points is the  same.....so....

 

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

 

x^2  + 6x  + 9  +  4   =  x^2   + 4x  + 4  +  4           rearrange  as

 

2x  +  5  =  0

 

2x  =  -5

 

x = -5/2

 

The  center is   (-5/2 , 0)

 

And the  radius =  sqrt   [ (-5/2 + 3)^2  +  4  ]   =  sqrt  (17/4)  =  sqrt (17)  / 2

 

Here's  a graph  :   https://www.desmos.com/calculator/sd3oslkkql

 

 

cool cool cool

 May 31, 2021

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