Question

Find points on the X-axis whose distance from the line x/3 + y/4 = 1 is 4 units.

Answer 1

The equation of line x/3 + y/4 = 1  

i.e. 4x + 3y – 12 = 0 …..(i) 

Let (h, 0) be a point on the X-axis. 

The distance of this point from line (i) is 4.

⇒ |4h – 12| = 20 

⇒ 4h – 12 = 20 or 4h – 12 = -20 

⇒ 4h = 32 or 4h = -8 

⇒ h = 8 or h = -2 

∴ The required points are (8, 0) and (-2, 0).