If the slope of a line passing through the point A(3, 2) is 3/4 then find points on the line which are 5 units away from the point A. 

Equation of the line passing through (3, 2) having slope 3/4 is

y - 2 = 3/4 (x - 3)

4y - 3x + 1 = 0                                      ... (1)

Let (h, k) be the points on the line such that

(h - 3)² + (k - 2)² = 25                           ... (2)

Also, we have

4k - 3h + 1 = 0                                      ... (3)

or k = ^{(3h - 1)}/₄

Putting the value of k in (2) and simplifying, we get

25h² - 150h - 175 = 0

or h² - 6h - 7 = 0

or (h + 1)(h - 7) = 0 ⇒ h = -1, h = 7

Putting these values of h in (4), we get k = -1 and k = 5.

Therefore, the coordinates of the required points are (-1, -1) or (7, 5).