Concept: Nutrition plays a vital role in maintaining health and physical performance. A balanced diet ensures the body receives adequate nutrients for proper functioning.
Definition of Balanced Diet: A balanced diet is a diet that provides all essential nutrients — carbohydrates, proteins, fats, vitamins, minerals, fiber, and water — in the right proportions to meet the body’s needs.
Components of a Balanced Diet:
Carbohydrates – energy source
Proteins – growth and repair
Fats – stored energy and insulation
Vitamins and minerals – body regulation
Fiber – digestive health
Water – metabolic activities
Importance of a Balanced Diet:
Provides Energy: Supplies fuel for daily activities and physical exercise.
Supports Growth and Development: Essential for children, adolescents, and athletes.
Boosts Immunity: Helps the body resist infections and diseases.
Maintains Healthy Body Weight: Prevents obesity and malnutrition.
Improves Overall Health: Enhances physical and mental performance.
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 \(P,O,Q\).