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: 

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

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, 

3x + y – 5 = 0 

⇒ y = - 3x + 5 

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

So, the equations of the required lines are

⇒ x + 2y – 8 = 0 and 2x – y – 1 = 0 

Hence, Equation of given line is x + 2y – 8 = 0 and 2x – y – 1 = 0