(i) Given,

equation of line L₁, is y = 4.

L₂ is the bisector of angle O and O = 90˚.

Thus, the line L₂ makes an angle of 45˚ with the x-axis.

Thus, slope of line L₂ = tan 45˚ = 1

(ii) The line L₂ passes through (0, 0) and its slope is 1. So, its equation is given by

y - y₁ = m(x - x₁)

Now, the point P is the point of intersection of the lines L₁ and L₂.

Solving the equations y = 4 and x = y, we get x = y = 4

Thus, the coordinates of the point P are (4, 4).

(iii) The line L₂ passes through (0, 0) and its slope is 1. So, its equation is given by

y - y₁ = m(x - x₁)

$\Rightarrow \mathrm{y} - 0 = 1(\mathrm{x} - 0)$

$\Rightarrow \mathrm{y} = \mathrm{x}$