Question

Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.

Answer 1

Let the slope of the required line be m1.
The given line can be written as y=1/2 x - 3/2 , which is of the form y = mx + c
∴Slope of the given line =m₂ = 1/2
It is given that the angle between the required line and line x – 2y = 3 is 45°.
We know that if θ is the acute angle between lines l₁ and l₂ with slopes m₁ and m₂ , then

Case I: m₁ = 3
The equation of the line passing through (3, 2) and having a slope of 3 is:
y – 2 = 3 (x – 3) y – 2 = 3x – 9
3x – y = 7
Case II: m₁ = - 1/3

The equation of the line passing through (3, 2) and having a slope of - 1/3 is:

Thus, the equations of the lines are 3x – y = 7 and x + 3y = 9.