The points (2,3) and (3,2) lie on a circle whose center is on the x-axis. What is the radius of the circle?
+36916 The center (h,0 ) is the same distance from each of the points (h,0) because it is on the x axis then y = 0
distance from point 1 to center h,0
sqrt [ (h-2)^2 + ( 0-3)^2 ]
distance from point 2 to center
sqrt [ (h-3)^2 + ( 0-2)^2 ] Now you have two equations, two unknowns ...solve for h,k
sqrt [ (h-2)^2 + ( 0-3)^2 ] = sqrt [ (h-3)^2 + ( 0-2)^2 ]
(h-2)^2 + (0-3)^2 = (h-3)^2 + ( 0-2)^2
h^2 -4h + 4 + 9 = h^2 -6h+9 + 4
-4h + 4 + 9 = -6h + 9 + 4
2h +13 = 13
2h = 0
h=0
So the center is 0,0 can you calculate the radius now? Need more help? (use distance formula from 0,0 to either of the points)
