+1839 Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$
+129885 All points 5 units away from (2,7) can be represented by a circle with the following equation
(x - 2)^2 + (y -7)^2 = 25
find the intersection of this circle with the line thusly
(x -2)^2 + (5x -28 - 7)^2 = 25
(x - 2)^2 + (5x - 35)^2 = 25
x^2 - 4x + 4 + 25x^2 - 350x + 1225 = 25
26x^2 - 354x + 1204 = 0
x = 86/13 and x = 7
y = 5(86/13) - 28 = 66/13 y = 5(7) - 28 = 7
The points are ( 86/13 , 66/13) and ( 7 , 7)
