To find:

The equation of the straight line which cuts off intercepts on x-axis twice that on y-axis and is at a unit distance from the origin.

Assuming:

Intercepts on x-axis and y-axis be 2a and a, respectively.

Explanation:

So, the equation of the line with intercepts 2a on x-axis and a on y-axis be

⇒ x + 2y = 2a … (1)

Let us change equation (1) into normal form.

Thus, the length of the perpendicular from the origin to the line (1) is

Given:

P = 1

Required equation of the line:

x + 2y

⇒ x + 2y + = 0

Hence, equation of required line is x + 2y + = 0.