Question

Find the equations to the straight lines passing through the point (2, 3) and inclined at an angle of 45° to the lines 3x + y – 5 = 0.

Answer 1

Given: 

The equation passes through (2, 3) and make an angle of 45° with the line 3x + y – 5 = 0.

We know that the equations of two lines passing through a point x₁,y₁ and making an angle α with the given line y = mx + c are

Here,
Equation of the given line is,

3x + y – 5 = 0

y = – 3x + 5

Comparing this equation with y = mx + c we get, m = – 3
x₁ = 2, y₁ = 3, α = 45°, m = – 3.

So, the equations of the required lines are

x + 2y – 8 = 0 and 2x – y – 1 = 0

∴ The equation of given line is x + 2y – 8 = 0 and 2x – y – 1 = 0