Find the equation of the straight line intersecting y – axis at a di

1.	Find the equation of the straight line intersecting y – axis at a distance of 2 units above the origin and making an angle of 30 0 with the positive direction of the x–axis.
Answer» Given, A line which intersects at y–axis at a distance of 2 units and makes an angle of 30° with the positive direction of x–axis. To Find: The equation of that line. Formula used: The equation of line is [y – y₁ = m(x – x₁)] Explanation: Here, Angle = 30° (Given) So, The slope of the line, m = tan θ m = tan 30° m = \(\frac{1}{\sqrt{3}}\) Now, The coordinates are (x₁, y₁) = (0, 2) The equation of line = y – y₁ = m(x – x₁) y – 2 = \(\frac{1}{\sqrt{3}}\) (x – 0) \(\sqrt{3y}\) + \(2\sqrt{3}\) = x \(\sqrt{3y}\) + \(2\sqrt{3}\) - x = 0 Hence, The equation of line is \(\sqrt{3y}\) + \(2\sqrt{3}\) - x = 0

Find the equation of the straight line intersecting y – axis at a distance of 2 units above the origin and making an angle of 30 0 with the positive direction of the x–axis.

Answer»

Given, A line which intersects at y–axis at a distance of 2 units and makes an angle of 30° with the positive direction of x–axis.

To Find: The equation of that line.

Formula used: The equation of line is [y – y₁ = m(x – x₁)]

Explanation: Here, Angle = 30° (Given)

So, The slope of the line, m = tan θ

m = tan 30°

m = \(\frac{1}{\sqrt{3}}\)

Now, The coordinates are (x₁, y₁) = (0, 2)

The equation of line = y – y₁ = m(x – x₁)

y – 2 = \(\frac{1}{\sqrt{3}}\) (x – 0)

\(\sqrt{3y}\) + \(2\sqrt{3}\) = x

\(\sqrt{3y}\) + \(2\sqrt{3}\) - x = 0

Hence, The equation of line is \(\sqrt{3y}\) + \(2\sqrt{3}\) - x = 0