Question

Find the equation of the line on which length of the perpendicular from the origin is 5 and the angle which this perpendicular makes with the x-axis is ${60}^{\circ }$.

• A. $x\sqrt{3}+2y+8=0$
• B. $x+\sqrt{2}y-7=0$
• C. $x+\sqrt{3}y=10$
• D. none of (a), (b), (c)

Answer 1

The correct option is C $x+\sqrt{3}y=10$

Here p = 5 and $\alpha ={60}^{\circ }$
$\therefore$ The required equation of the line is
x cos $\alpha +y$ sin $\alpha =p$
or $xcos{60}^{\circ }+ysin{60}^{\circ }=5$
$\Rightarrow x+\sqrt{3}y=10(\because sin{60}^{\circ }=\frac{\sqrt{3}}{2}andcos{60}^{\circ }=\frac{1}{2})$