Question

find the equation of the lines through (3,2) which makes an angle 45 degree with the line x-2y=3​

Answer 1

Step-by-step explanation:

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 ,

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.