Question

Combined equation of the lines bisecting the angles between the coordinate axes, is ______.

Options

• x² + y² = 0

• xy = 0

• x(x – y) = 0

• x² – y² = 0

Answer 1

Combined equation of the lines bisecting the angles between the coordinate axes, is x² – y² = 0.

Explanation:

Let the lines OA and OB bisect the angles between the coordinate axes

∴ Slopes of OA = tan 45°

= 1 and slope of OB

= tan (– 45°)

= – 1

∴ Equations of OA and OB are

y = x

and y = – x

Combined equation is (x + y)(x – y) = 0

i.e. x² – y² = 0