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प्रश्न
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.
Find the equation of a line intersecting the 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.
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उत्तर
Let m be the slope of the required line,
m = tan θ
= tan 30°
∴ m = `1/sqrt3`
Here, c = y − intercept = 2
Substituting the values of m and c in y = mx + c, we get:
\[y = \frac{1}{\sqrt{3}}x + 2 \]
\[\sqrt{3}y = x + 2\sqrt{3}\]
\[ \Rightarrow x - \sqrt{3}y + 2\sqrt{3} = 0\]
Hence, the equation of the required line is \[x - \sqrt{3}y + 2\sqrt{3} = 0\].
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