Question

The equations of the lines through the origin making an angle of $60 ^ { \circ }$ with the line $x + y \sqrt { 3 } + 3 \sqrt { 3 } = 0$ are.

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

Answer 1

Answer: (B)

$x = 0 , x - y \sqrt { 3 } = 0$

Answer 2

Since the line $x + y \sqrt { 3 } + 3 \sqrt { 3 } = 0$ makes an angle of $150 ^ { \circ }$with $x$-axis. Therefore, the required lines will make angles of $90 ^ { \circ }$and $210 ^ { \circ }$ i.e., $30 ^ { \circ }$with the positive direction of x-axis.

Hence the lines are $x = 0$ and $y = \frac { 1 } { \sqrt { 3 } } x$.