Question

The equations of the lines passing through the point

(1, 0) and at a distance $\frac { \sqrt { 3 } } { 2 }$ from the origin, are.

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

Answer 1

Answer: (A)

Answer 2

The equation of lines passing through (1, 0) are given by $y = m ( x - 1 )$. Its distance from origin is $\frac { \sqrt { 3 } } { 2 }$ .

⇒ $\left| \frac { - m } { \sqrt { 1 + m ^ { 2 } } } \right| = \frac { \sqrt { 3 } } { 2 }$ ⇒ $m = \pm \sqrt { 3 }$ . Hence the lines are

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