Identify the given image of ancient temple from the given options: 
Kailashnath Temple: The image shows the Kailashnath Temple which is an important example of rock cut architecture at Ellora in Maharashtra. It is notable for its monolithic structure which was carved out of a single rock.
Deogarh Temple: The Deogarh temple is a Gupta era temple located in Uttar Pradesh, known for its distinct architectural style.
Brihedeshwara Temple: The Brihedeshwara Temple is a Chola era temple and is located in Thanjavur.
Mahabalipuram Temple: The Mahabalipuram temple complex is known for its rock-cut architecture and is located in Tamil Nadu.
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 \(P,O,Q\).