When a steady current flows through a long straight wire, the magnetic field lines form concentric circles around the wire, as per Ampere’s Law. The direction of the magnetic field lines follows the right-hand rule: if you curl the fingers of your right hand around the wire in the direction of the current, your thumb points in the direction of the magnetic field.
Therefore, for a vertical current-carrying wire, the magnetic field lines will be horizontal and form concentric circles around the wire.
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 \(P,O,Q\).