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 :

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Mathematics

Various Form of a Straight Line

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 :

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

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

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

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

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Let the slope of the line is m

$\tan 60 ° = | \frac{m + \sqrt{3}}{1 - \sqrt{3} m} |$

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

$So, m + \sqrt{3} = \pm \sqrt{3} (1 - \sqrt{3} m)$

As line intersects x-axis

So line will be, $y - \sqrt{3} x + 2 + 3 \sqrt{3} = 0$

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