Find the equation of the line, which passes through the point (2, 3) a

1.	Find the equation of the line, which passes through the point (2, 3) and makes an angle of 30° with the positive direction of x-axis.
Answer» Given, inclination of the line, θ = 30°. Slope of the line, m = tan 30° = \(\frac{1}{\sqrt{3}}\) Equation of a line in one-point form is y – y₀ = m(x – x₀) Since m = \(\frac{1}{\sqrt{3}}\) and (x₀, y₀) = (2, 3) ∴ y − 3 = \(\frac{1}{\sqrt{3}}\)(x − 2) ⇒ \(\sqrt{3}\)y − 3\(\sqrt{3}\) = x – 2 ⇒ x − \(\sqrt{3}\)y + (2 − 3\(\sqrt{3}\)) = 0, is the required equation of the line.

Find the equation of the line, which passes through the point (2, 3) and makes an angle of 30° with the positive direction of x-axis.

Answer»

Given, inclination of the line, θ = 30°.

Slope of the line, m = tan 30°

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

Equation of a line in one-point form is

y – y₀ = m(x – x₀)

Since m = \(\frac{1}{\sqrt{3}}\) and (x₀, y₀) = (2, 3)

∴ y − 3 = \(\frac{1}{\sqrt{3}}\)(x − 2)

⇒ \(\sqrt{3}\)y − 3\(\sqrt{3}\) = x – 2

⇒ x − \(\sqrt{3}\)y + (2 − 3\(\sqrt{3}\)) = 0, is the required equation of the line.