Browse Questions

# Choose the correct answer from the given four options. The equations of the lines passing through the point (1, 0) and at a distance $\large\frac{\sqrt 3 }{2}$ from the origin, are

$\begin {array} {1 1} (A)\;\sqrt 3 x + y - \sqrt 3 = 0, \sqrt 3 x - y - \sqrt 3 = 0 & \quad (B)\;\sqrt 3 x + y + \sqrt 3 = 0, \sqrt 3 x - y + \sqrt 3 = 0 \\ (C)\;x+ \sqrt 3 \: y - \sqrt 3 =0, x - \sqrt 3 y - \sqrt 3 = 0 & \quad (D)\;\text{None of these} \end {array}$

Toolbox:
• Distance of a line $ax+by+c=0$ from the origin (0,0) is $d = \bigg| \large\frac{c}{\sqrt{A^2+B^2}} \bigg|$
Step 1 :
It is given tht the line passes through the point (1,0) and its distance from the origin is $\large\frac{\sqrt 3 }{2}$
Consider the option 'A'
$\sqrt 3 (1)+(0)-\sqrt 3 =0, \: \sqrt 3 (1) - 0 - \sqrt 3 =0$
LHS = RHS