(a) Define the following:
(i) Enantiomers
(ii) Racemic mixture
(i) Enantiomers:
Enantiomers are a pair of stereoisomers that are non-superimposable mirror images of each other. They have identical physical and chemical properties except for their interaction with plane-polarized light (optical activity) and reactions with other chiral molecules. Enantiomers rotate plane-polarized light in equal magnitudes but opposite directions (one being dextrorotatory [+] and the other levorotatory [−]).
Example: The two forms of lactic acid (D-lactic acid and L-lactic acid) are enantiomers.
(ii) Racemic Mixture:
A racemic mixture (or racemate) is a 1:1 mixture of two enantiomers of a chiral molecule. Because the optical activities of the enantiomers cancel each other out, a racemic mixture is optically inactive (does not rotate plane-polarized light). Racemic mixtures are often formed in chemical reactions where a chiral product is generated from achiral reactants without the use of a chiral catalyst or enzyme.
Example: Racemic tartaric acid is an equal mixture of D-tartaric acid and L-tartaric acid.

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 \(P,O,Q\).