A straight line L at a distance of 4 units from the origin makes positive intercepts on th…

Question

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

Accepted Answer

The equation of line is

x cos $$\theta $$ + y sin $$\theta $$ = p

$$ \Rightarrow $$ x cos (75o) + y sin (75o) = 4

$$ \Rightarrow $$ $$x\left( {{{\sqrt 3  - 1} \over {2\sqrt 2 }}} \right) + y\left( {{{\sqrt 3  + 1} \over {2\sqrt 2 }}} \right) = 4$$

$$ \Rightarrow $$ $$x\left( {\sqrt 3  - 1} \right) + y\left( {\sqrt 3  + 1} \right) = 8\sqrt 2 $$

Solutions · 1