The points on the straight line 3 x-4 y+1=0 which are at a distance of 5 units from the point (3,2) are

Step-by-step solution

Let the point A(x, y) on the line 3 x-4 y+1 is at distance 5 units from the point (3,2) . x₁-3 = y₁-2 = 5 Since, (x₁, y₁ ) lies on the line 3 x-4 y-1=0 array ll & 3(3 5 )-4(2 5 )-1=0 & 9 15 -8+20 -1=0 & 15 -20 =0 & 3 = 4 = 3 / 4 & = 4 / 5 = 3 / 5 array From Eqs. (i) and (ii), we get aligned & x₁=3 ( 4 5 ) 5=7,-1 & y₁=2 5 ( 3 5 )=5,-1 aligned Coordinates are (7,5) and (-1,-1)