Find the equation of the line passing through (2, 2√3) and inclined

1.	Find the equation of the line passing through (2, 2√3) and inclined with x – axis at an angle of 75°
Answer» Given: A line which is passing through (2, 2√3), the angle is 75°. By using the formula, The equation of line is [y – y₁ = m(x – x₁)] Here, angle, θ = 75° The slope of the line, m = tan θ m = tan 75° = 3.73 = 2 + √3 The line passing through (x₁, y₁) = (2, 2√3) The required equation of the line is y – y₁ = m(x – x₁) Now, substitute the values, we get y – 2√3 = 2 + √3 (x – 2) y – 2√3 = (2 + √3)x – 7.46 (2 + √3)x – y – 4 = 0 ∴ The equation of the line is (2 + √3)x – y – 4 = 0

Find the equation of the line passing through (2, 2√3) and inclined with x – axis at an angle of 75°

Answer»

Given:

A line which is passing through (2, 2√3), the angle is 75°.

By using the formula,

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

Here, angle, θ = 75°

The slope of the line, m = tan θ

m = tan 75°

= 3.73 = 2 + √3

The line passing through (x₁, y₁) = (2, 2√3)

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

Now, substitute the values, we get

y – 2√3 = 2 + √3 (x – 2)

y – 2√3 = (2 + √3)x – 7.46

(2 + √3)x – y – 4 = 0

∴ The equation of the line is (2 + √3)x – y – 4 = 0