Question

Find the equations to the straight lines which pass through the point (h, k) and are inclined at angle tan^-1 m to the straight line y = mx + c.

Answer 1

Given: 

equation passes through (h, k) and make an angle of tan^-1 m with the line y = mx + c 

To find: 

equation of given line

Explanation: 

We know that the equations of two lines passing through a point x₁,y₁ and making an angleα with the given line y = m ’x + c are 

m’ = m so,

 y - y₁ = \(\frac {m±\,tan\ \,\alpha}{1±m\,tan\ \,\alpha}\) (x - x₁)

Here,x₁ = h, y₁ = k, α = tan^-1 m’ = m. 

So, the equations of the required lines are