Find the equation of the line through (-2, 1) in symmetric form

Question

Find the equation of the line through (-2, 1) in the symmetric form when the angle made by the line with the positive direction  of x-axis is 45°.

Answer 1

We know that the equation of the line in symmetric form passing through the point (x1, y1) and making an angle 0 with the positive direction of x-axis is:

    [x - x₁] / cos 0 = [y - y₁] / sin 0

Here, x₁ = -2 , y_{​​​​​1} = 1 and 0 = 45°, therefore, required equation of the line is:

[x + 2] / cos 45° = [y - 1] / sin 45°

x + 2 = y - 1      {•.• cos 45° = sin 45°}