+866 Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.
+128578 x + y = 13
y = 13 - x
We have a circle with a radius of 5 and a center of (2,7).....the equation is
(x - 2)^2 + (y - 7)^2 = 25
(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 + 25 = 0
x = [ 16 ± sqrt [ 256 - 200] ] / 4 = [ 16± sqrt [ 56 ] ] / 4 =
x = [ 8 + sqrt 14 ] / 2 and x = [ 8 - sqrt 14 ] ] / 2
x = 4 + sqrt [14 ] / 2 and x = 4 -sqrt [14 ] / 2
y = 13 - x
y = 9 - sqrt [14] / 2 and y = 9 + sqrt [14] / 2
The points are ( 4 + sqrt [ 14] / 2 , 9 - sqrt [14] / 2) and (4 -sqrt [14] / 2 , 9 + sqrt [14] / 2)
