Question

The perpendicular distance of a line from origin is 2 units and the perpendicular makes an angle α with X-axis such that sin α=13. The equation of line is .

• A. $2\sqrt{2}x+y=6$
• B. $2\sqrt{2}x-y=6$
• C. $x+2\sqrt{2}y=6$
• D. $x-2\sqrt{2}y=6$

Answer 1

The correct option is A $2\sqrt{2}x+y=6$

$\mathrm{Perpendicular}\mathrm{distance},p=2\mathrm{Given},\sin \alpha =\frac{1}{3}\Rightarrow \cos \alpha =\pm \sqrt{1-{\sin }^2\alpha }=\pm \sqrt{1-\frac{1}{9}}=\pm \frac{2\sqrt{2}}{3}\mathrm{Hence},\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{by}\mathrm{normal}\mathrm{form}\mathrm{is}\pm \frac{2\sqrt{2}x}{3}+\frac{y}{3}=2\Rightarrow 2\sqrt{2}x+y=6\mathrm{or}-2\sqrt{2}x+y=6$