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Question
Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.
Solution
The graph of the required line is shown below.
The line which is inclined at an angle of 60° with the positive direction of y-axis makes an angle of 30° with x-axis.
Clearly, the slope of the required line is \[m = \tan {30}^\circ = \frac{1}{\sqrt{3}}\]
So, the equation of the required line having slope \[\frac{1}{\sqrt{3}}\] and passes through the point \[P\left( 3, - 2 \right)\] is
\[y + 2 = \frac{1}{\sqrt{3}}\left( x - 3 \right)\]
\[ \Rightarrow x - \sqrt{3}y - 3 - 2\sqrt{3} = 0\]
Hence, the equation of the required line is \[x - \sqrt{3}y - 3 - 2\sqrt{3} = 0\]
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