Question

Given a straight line x cos 30° + y sin 30° = 2. Determine the equation of the other line which is parallel to it and passes through (4, 3).

Answer 1

x cos 30° + y sin 30° = 2

`=> x sqrt(3)/2 + y + 1/2 = 2`

`=> sqrt(3)x + y = 4`

`=> y = -sqrt(3)x + 4`

Slope of this line = `-sqrt(3)`

Slope of a line which is parallel to this given line = `-sqrt(3)`

Let (4, 3) = (x₁, y₁)

Thus, the equation of the required line is given by :

 y – y₁ = m(x – x₁)

`=> y - 3 = -sqrt(3) (x - 4) = -sqrt(3)x + 4sqrt(3)`

`=> sqrt(3)x + y = 4sqrt(3) + 3`