Coulomb repulsion between protons in the nucleus arises because protons are positively charged and like charges repel each other. If this repulsion were not countered, the nucleus would not be stable. This Coulomb repulsion is overcome by the **strong nuclear force**, which is a force that acts between nucleons (protons and neutrons) and is much stronger than the Coulomb force at short distances (on the order of 10−15 meters). The strong nuclear force is attractive, and it binds protons and neutrons together within the nucleus. At very short distances, the strong nuclear force is strong enough to overcome the repulsive Coulomb force between protons, ensuring the stability of the nucleus. This is why nuclei, despite the Coulomb repulsion between protons, can remain stable.

A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).