Question

Find the equations to the straight lines which pass through the origin and are inclined at an angle of 75° to the straight line x + y + √3(y - x) = a.

Answer 1

Given: 

Equation passes through (0,0) and make an angle of 75° with the line x + y + √3(y - x) = a.

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 = mx + c are

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

Here, Equation of the given line is,

Comparing this equation with y = mx + c 

We get,

and tan75^∘ = 2 + √3

So, the equations of the required lines are

Hence, Equation of given line is x = 0 and √3x +y = 0