Question

Find the equations of the bisector of the angles between the straight line 3x+4y+7=0 and 12x+5y-8=0.

Answer 1

If the constant terms are both positive then the given equations will be written as

3x - 4y + 7 = 0 and -12x + 5y + 8 = 0

The equation to the bisector of the angle in which the origin lies is

Or 13(3x - 4y + 7) = 5(-12x + 5y + 8)

Or 99x - 77y + 51 = 0

The equation to the other bisector is

Or 13(3x - 4y + 7) = -5(-12x + 5y + 8)

Or 13(3x - 4y + 7) + 5(-12x + 5y + 8) = 0

Or 21x + 27y - 131 = 0.