+1911 Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.
+129852 (x - 2)^2 + (y - 7)^2 = 25 (1)
x + y = 13 → y = 13 - x (2)
Sub (2) into (1)
(x -2)^2 + ( 13-x -7)^2 = 25
(x-2)^2 + ( 6 -x)^2 = 25
x^2 - 4x + 4 + x^2 -12x + 36 = 25
2x^2 -16x + 40 = 25
2x^2 - 16x + 15 = 0
x = [ 16 + sqrt [ 16^2 - 4*2 * 15 ] ] / 4 and x = 4 - sqrt (136) /4
x = [16 + sqrt [ 136] ] / 4 = 4 + sqrt (136)/4 y = 9 + sqrt (136)/4
y = 13 - x = 9 - sqrt (136)/4
(x , y) = ( 4 + sqrt (136) / 4 , 9 -sqrt (136)/4) and ( 4 -sqrt (136)/4 , 9 + sqrt (136) / 4)
