Find the equations to the straight lines passing through the point (2, 3) and inclined at an angle of 450 to the lines 3x + y – 5 = 0.
Given: equation passes through (2,3) and make an angle of 450with 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 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
Hence, Equation of given line is x + 2y – 8 = 0 and 2x – y – 1 = 0