A straight line L through the point ( 3 , - 2 ) is inclined at an angle 60 to the line 3 x + y = 1 . If L also intersects the x -axis, then the equation of L is [2011]

Question

A straight line $L$ through the point $(3, - 2)$ is inclined at an angle $60 °$ to the line $\sqrt{3} x + y = 1$ . If $L$ also intersects the $x$ -axis, then the equation of $L$ is [2011]

Smart Achievers · Accepted Answer

(2)

Let the slope of line $(3, - 2)$ be $m$ . Then

$| \frac{m + \sqrt{3}}{1 - \sqrt{3} m} |$ $= \sqrt{3}$

$L$

$\Rightarrow 4 m = 0 or 2 m = 2 \sqrt{3} \Rightarrow m = 0 or m = \sqrt{3}$

$∵$ $L intersects x -axis,$ $∴$ $m = \sqrt{3}$

$∴$ $Equation of L is y + 2 = \sqrt{3} (x - 3)$

$\Rightarrow \sqrt{3} x - y - (2 + 3 \sqrt{3}) = 0$

Solution

Q.
A straight line $L$ through the point $(3, - 2)$ is inclined at an angle $60 °$ to the line $\sqrt{3} x + y = 1$ . If $L$ also intersects the $x$ -axis, then the equation of $L$ is [2011]

1 $y + \sqrt{3} x + 2 - 3 \sqrt{3} = 0$

2 $y - \sqrt{3} x + 2 + 3 \sqrt{3} = 0$

3 $\sqrt{3} y - x + 3 + 2 \sqrt{3} = 0$

4 $\sqrt{3} y + x - 3 + 2 \sqrt{3} = 0$

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Solution

Q. A straight line L through the point (3, -2) is inclined at an angle 60° to the line 3x+y=1. If L also intersects the x-axis, then the equation of L is [2011]

1 y+3x+2-33=0

2 y-3x+2+33=0

3 3y-x+3+23=0

4 3y+x-3+23=0