Let the equation (1) represent the two straight lines
L1OM1 and L2OM2 inclined at angles θ1 and θ2 to the axis of x, so that (1) is equivalent to
Let OA and OB be the required bisectors.
Hence, if θ stand for either of the angles AOX or BOX, we have
by equations (2).
But, if (x, y) be the coordinates of any point on either of the lines OA or OB, we have
This, being a relation holding between the coordinates of any point on either of the bisectors, is the equation to the bisectors.
