Meera Ltd. is registered with an authorised capital of ₹ 1,00,000 divided into equity shares of ₹ 10 each. The company invited applications for issuing 1,00,000 equity shares at a premium of ₹ 2 per share. The amount was payable as follows:
Applications were received for 95,000 shares and allotment was made to all the applicants. All calls were made and duly received except the second and final call of 1,000 shares held by Tushar.
Answer the following questions:
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 \(P,O,Q\).