1.1. The village of Camberwick Green lies on a straight road, as modelled by the line $y=x$ on the graph below, measured in miles. Rush hour traffic through the village causes both congestion and air pollution.To ease congestion and improve the air quality around Camberwick Green a bypass ,modelled by part of the equation

$y=1+2ln({x}^{2})$

is to be built.

The bypass is to be built with a roundabout south of the village at point $S$ and a northern roundabout which re-joins the road through Camberwick Green at the point $P(p,p)$.

Write down the coordinates of the southern roundabout at point $S$.

1.2. (i) Draw a staircase diagram on the graph in part (a) to how an iteration formula with a starting value of ${x}_{0}$ in the interval $[1,p]$ will converge to the northern roundabout at point $P$.

(ii) Use a suitable iteration formula with an initial value of ${x}_{0}=10$ to find the value of $p$ to 5 significant figures.

1.3. Find the length of road through Camberwick Green that will benefit from the construction of the bypass.