Two lines are represented by the equations y-x=6 and x+y=8. A point has to be marked so that it is at a distance of 100 from each of the lines. FInd the possible location of the point.

Since The distance from a point (m,n) to the line Ax+By+C= 0is given by:
d = (|Am + Bn + C|)/ sqrt(A²+B²). Therefore using the condition as given in the question (the point is equidistance from the two lines and the distance is equal to 100). We can solve the two equations and can easily get the point (m,n) = (1, 7+100sqrt(2)).