Find the points on the x-axis whose perpendicular distance from the straight line  x/a + y/b = 1  is a. 

Let (x₁, 0) be any point on x-axis.

Equation of the given line is bx + ay - ab = 0.The perpendicular distance of the point (x₁, 0) from the given line is

a = ±^{(bx₁ + a0 - ab)}/_{√(a² + b²)}

∴ x₁ = ^a/_b(b ± √(a² + b²))

Thus, the point on x-axis is

(^a/_b(b ± √(a² + b²)),0)