Question

Question 5 Find the points on the x-axis, whose distances from the line are 4 units.

Class X1 - Maths -Straight Lines Page 227

Answer 1

Let (P, 0) is the point on x-axis whose distance from the line x/3 + y/4 = 1 are 4 units.
now, equation of line is x/3 + y/4 = 1
or, 4x + 3y = 12
or, 4x + 3y - 12 = 0

use formula,
the distance of the point (h,k) from the line ax + by+c = 0 is d = |ah + bk + c |/√(a² + b²)

so, 4 = |4 × h + 3 × 0 - 12|/√(4² + 3²)
4 = | 4h - 12 |/5
20 = |4h - 12|
±20 = 4h - 12

taking positive sign,
20 = 4h - 12
32 = 4h
h = 8

taking negative sign,
-20 = 4h - 12
- 8 = 4h
h = -2
hence, points on the x-axis. are ( 8,0) and (-2,0)