+865 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?
+23 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!
