+641 Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$
+37084 The set of points 5 units away from 2,7 is a circle :
(x-2)^2 + (y-7)^2 = 5^2
The line might intersect at ONE point (tangent) or TWO Points .
Plug in the value of the line into the circle equation
( x-2)^2 + ( 5x-28 -7)^2 = 5^2
Expand
x^2 - 4x + 4 + 25x^2 -350x + 1225 = 25
Solve for 'x'
26x^2 - 354 x + 1204 = 0 Use quadratic formula to find x = 7 and 6.61538 ( two points) ....use these values ofr 'x' in the line equation to find the corresponding ' y ' coordinates = 7 and 5.07692
