Question

Find the equations of straight lines passing through (2, -1) and making an angle of 45° with the line 6x + 5y – 8 = 0.

Answer 1

Given: 

The equation passes through (2, -1) and make an angle of 45° with the line 6x + 5y – 8 = 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,

6x + 5y – 8 = 0

5y = – 6x + 8

y = -6x/5 + 8/5
Comparing this equation with y = mx + c

We get, m = -6/5 

Where, x₁ = 2, y₁ = – 1, α = 45°, m = -6/5

So, the equations of the required lines are

x + 11y + 9 = 0 and 11x – y – 23 = 0

∴ The equation of given line is x + 11y + 9 = 0 and 11x – y – 23 = 0