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Question
Find the equation of the line which satisfy the given condition:
Intersects 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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Solution
The point located at a distance of 2 units on the y-axis from the origin will be (0, 2). The line makes an angle of 30° with the positive direction of the x-axis.
∴ m = tan 30° = `1/sqrt3`
equation of line,
y – y1 = m (x – x1)
y – 2 = `1/sqrt3 ("x" - 0)`
or `sqrt3"y" - 2sqrt3 = "x"`
or `"x" - sqrt3"y" + 2 sqrt3 = 0`
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