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This circle passes through the points (-1, 2), (3,2) and (9,0). The center of the circle is at (h,k). What is the value of h+k?

 Jul 4, 2022
 #1
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The form is  (x - h)^2 + (y - k)^2 = r^2

 

Using the first two points and the square of the distance formula to equate the radius's we have

 

(-1-h)^2  + ( 2 - k)^2 =    (3-h)^2 + (2 - k)^2

 

h^2 + 2h + 1  =  h^2 - 6h + 9

 

8h  =  8

 

h =  1   this is the x coordinate of the center

 

Using the last two points and doing the  same thing we have

 

(3 - 1)^2 + (2 - k)^2  = (9 - 1)^2  + (0 - k)^2

 

4 + k^2 -4k + 4  =  64  + k^2

 

-4k + 8 =  64

 

-4k  = 56

 

k= -14

 

 

h +  k =    1  - 14  =     -13

 

 

cool cool cool

 Jul 4, 2022

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