Question

Find the coordinates of the points on a line 3x-4y=1 which are 5 units away from 3,2 which is also on the line

Answer 1

call the point (a,b) then you know
\[(a-3)^2+(b-2)^2=25\] and
\[3a-4b=1\] solve these simultaneously get
\[(-1,-1),(7,5)\]

Answer 2

5 is the hypoteneuse of a 3,4,5 triangle (slope is 3/4) so

the points are (3,2) +- (4,3)