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A circle is centered at (5,15) and has a radius of sqrt130 units. Point Q = (x,y) is on the circle, has integer coordinates, and the value of the x-coordinate is equal to the value of the y-coordinate. What is the maximum possible value for x?

 Jun 29, 2022
 #1
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Since x =  y ,  need to solve this

 

(x - 5)^2 + ( x - 15)^2  = 130

 

x^2 - 10x + 25 + x^2 - 30x + 225  = 130

 

2x^2 -40x + 120  =  0     divide through by 2

 

x^2 - 20x + 60  = 0

 

x^2 - 20x  =  - 60       complete the square on  x

 

x^2 -20x + 100 = -60 + 100

 

(x - 10)^2  = 40        take the positive root

 

x -10 =   sqrt (40)

 

x =  10 + sqrt (40) =   10 + 2sqrt (10) ≈  16.325 

 

 

cool cool cool

 Jun 29, 2022

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