Question

Eqnations of angle bisectors between two lines

Answer 1

The eqnations of the bisectors of the angles between the lines a₁ x+b₁ y+c₁ = 0 and a₂ x+b₂ y+c₂ =0 are given by

i. Any point on a bisector is equidistant from the given lines.

ii. Locus of points which are equidistant from the two intersecting lines is an angle bisector.

iii. Bisectors are perpendicular to each other.

iv. Equation of the bisector of the acute and of obtuse angle between two lines.

Let a₂ x+b₂ y+c₂ = 0 ......(1)

and a₂ +b₂ y+c₂ =0 ......(2)

c₁ >0,c₂ >0 then the equation

is the bisector of the acute or obtuse angle between the lines 1&2 according as a₁ a₂ +b₁ b₂ < 0 or > 0

again

is the bisector of the acute or obtuse angle between the lines 1&2 according as a₁ a₂ +b₁ b₂ > 0 or < 0