Name the oxometal anions of the first series of the transition metals in which the metal exhibits the oxidation state equal to its group number.
(i) Vanadate, VO3-
Oxidation state of V is + 5.
(ii) Chromate, CrO42-
Oxidation state of Cr is + 6.
(iii) Permanganate, MnO4-
Oxidation state of Mn is + 7.
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 \(P,O,Q\).