Question

Equation(s) or the straight line(s), inclined at ${30}^{\circ }$ to the $x-$axis such that the length of its (each of their) line segment(s) between the coordinate axes is $10$ units is/are

• A. $x+\sqrt{3}y+5\sqrt{3}=0$
• B. $x-\sqrt{3}y+5\sqrt{3}=0$
• C. $x+\sqrt{3}y-5\sqrt{3}=0$
• D. $x-\sqrt{3}y-5\sqrt{3}=0$

Answer 1

Answer: (B), (D)

$x-\sqrt{3}y+5\sqrt{3}=0$
$x-\sqrt{3}y-5\sqrt{3}=0$

Let the equation be $y=\frac{1}{\sqrt{3}}x+c$
the line cut the axes at $A(-\sqrt{3}c,0)$ and $B(0,c)$
Therefore $A{B}^2=c^2+3c^2=4c^2=100$
$⟹c=\pm 5$
so equations are $x-\sqrt{3}y\pm 5\sqrt{3}=0$