Question

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular drawn from the origin to this line makes an angle of 60° with the line \( x + y = 0 \). Then the equation of the line L is:

• A. \( (\sqrt{3}+1)x + (\sqrt{3}-1)y = \frac{8}{\sqrt{2}} \)
• B. \( (\sqrt{3}-1)x + (\sqrt{3}+1)y = \frac{8}{\sqrt{2}} \)
• C. \( \sqrt{3}x + y = \frac{8}{\sqrt{2}} \)
• D. \( x + \sqrt{3}y = 8\sqrt{2} \)

Hint:

For problems involving distances from the origin and angles with lines, use the general form of the line equation in terms of slope and intercepts.

Answer 1

The Correct Option is B

The equation of the line is derived by using the given conditions: the distance of the line from the origin and the angle it makes with the line \( x + y = 0 \). The result is \( (\sqrt{3}-1)x + (\sqrt{3}+1)y = \frac{8}{\sqrt{2}} \).