| Motivation | Inspiration |
|---|---|
| Comes from external sources like rewards, recognition, or pressure. | Comes from within the individual based on values or purpose. |
| Short-term influence to achieve specific goals. | Long-term and deeply rooted drive to act or create. |
| May need to be repeated frequently to maintain performance. | Usually sustains effort without repeated triggers. |
| Often task- or goal-oriented. | Often emotion- or vision-driven. |
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 \(P,O,Q\).