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Question
Find the equation of the strainght line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.
Solution
Let m be the slope of the required line.
\[\therefore m = \tan\theta = \tan {30}^\circ = \frac{1}{\sqrt{3}}\]
\[\text { Here, c = y - intercept }= 2\]
Substituting the values of m and c in y = mx + c, we get:
\[y = \frac{1}{\sqrt{3}}x + 2 \]
\[ \Rightarrow x - \sqrt{3}y + 2\sqrt{3} = 0\]
Hence, the equation of the required line is \[x - \sqrt{3}y + 2\sqrt{3} = 0\] .
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