Question

The equation of lines on which the perpendicular from the origin makes ${30}^o$ angle with x-axis and which form a triangle of area $\frac{50}{\sqrt{3}}$ with the axis are-

• A. $x\pm \sqrt{3}y-10=0$
• B. $\sqrt{3}x+y\mp 10=0$
• C. $x+\sqrt{3}y\pm 10=0$
• D. None of these

Answer 1

Answer: (B)

$\sqrt{3}x+y\mp 10=0$

equation of line,

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

$x\cos 30+y\sin 30=p$

$x\frac{\sqrt{3}}{2}+y\frac{1}{2}=p$

$x\sqrt{3}+y=2p$.........(i)

$A(\frac{2p}{\sqrt{3}},0),B(0,2p)$

$Area=\frac{1}{2}\times \frac{2p}{\sqrt{3}}\times 2p=\frac{50}{\sqrt{3}}$

$2p^2=50$

$p=\pm 5$

From (i)

$\sqrt{3}x+y=\pm 10$

$\sqrt{3}x+y\mp 10=0$