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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 twice the value of the y-coordinate. What is the maximum possible value for x?

 Jun 2, 2020
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the equation of the circle you described is

(x-5)2+(y-15)2=130

we are also told that

x = 2y

now all we do is substitute in 2y for x and solve:

(2y-5)2+(y-15)2=130

4y2-20y+25+y2-30y+225=130

y2-10y+50=26

y2-10y+24=0

(y-4)(y-6)=0

so y=4 or y=6

but since we are looking for the maximum value of x, and 2y=x, we want the larger y, 6.

Plugging this into 2y=x, we get

2(6)=x

x=12

 

Hope this solution is helpful!

 Jun 2, 2020

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