Identify the name of a woman devotee of early Bhakti tradition with the help of information given below:
• She was a devotee of Lord Shiva.
• She adopted a path of extreme asceticism to attain her goal.
Karaikkal Ammaiyar: Karaikkal Ammaiyar was a Tamil saint and Nayanar (devotee of Lord Shiva) known for her intense devotion and extreme asceticism (severe self-discipline) which she adopted as a path to salvation. She is one of the most revered figures among the Nayanars and her devotional poetry is very famous.
Mirabai: Mirabai was a devotee of Krishna who is known for her songs and bhajans in the Bhakti tradition. Her approach was not always ascetic but more of a love and devotion for Krishna.
Andal: Andal was an Alvar (devotee of Vishnu), known for her devotion and her poems that express her love for the deity.
Muktabai: Muktabai was a saint from Maharashtra in the Varkari tradition. She was not a devotee of Lord Shiva.
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 \(P,O,Q\).