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Question
Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.
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Solution
Given that the line makes angle 30° with y-axis
∴ Angle made by the line with x-axis is 60°
∴ Slope of the line
m = tan 60°
⇒ m = `sqrt(3)`
So, the equation of the line passing through the point (1, 2)
And slope `sqrt(3)` is y – y1 = m(x – x1)
⇒ y – 2 = `sqrt(3)(x - 1)`
⇒ y – 2 = `sqrt(3)(x - 1)`
⇒ `y - sqrt(3)x + sqrt(3) - 2` = 0
Hence, the required equation of line is `y - sqrt(3)x + sqrt(3) - 2` = 0
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