Under the Transfer of Property Act, 1882 a mortgage is a transfer of an interest in specific immovable property for securing the payment of a debt. Section 58 of the Act enumerates six distinct types of mortgages, each characterized by unique rights and obligations of the mortgagor and mortgagee. These categories reflect the balance of right of alienation and right to hold the property, contingent upon the nature of the transfer. In a simple mortgage, the mortgagor binds himself personally to repay the debt and agrees, expressly or impliedly, that in the event of default, the mortgagee shall have the right to cause the mortgaged property to be sold. There is no transfer of possession.
A mortgage by conditional sale involves an ostensible sale with a condition that upon default of payment, the sale becomes absolute. Courts scrutinize such arrangements to prevent clogs on the equity of redemption. A usufructuary mortgage grants the mortgagee possession and the right to receive rents and profits in lieu of interest or principal, aligning with the maxim, nemo dat quod non habet. It is essential to note that an earlier mortgage takes precedence based on the legal maxim, qui prior est tempore potior est jure. An English mortgage entails personal liability of the mortgagor and an absolute transfer of the property to the mortgagee with a covenant to retransfer upon payment. Other forms include mortgage by deposit of title deeds or equitable mortgage, and anomalous mortgages, which do not fit into the above classifications. These variations reveal the nuanced jurisprudence of secured transactions, balancing contractual freedom with equitable oversight.
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 \(P,O,Q\).