Sangeeta is a Python programmer working in a computer hardware company. She has to maintain the records of the peripheral devices. She created a csv file named Peripheral.csv to store the details. Structure of Peripheral.csv:
\begin{tabular}{|c|c|c|} \hline \textbf{P\_id} & \textbf{P\_name} & \textbf{Price} \\ \hline \end{tabular}
P\_id is the Peripheral device ID (integer).P\_name is the Peripheral device name (string).Price is the Peripheral device price (integer).Sangeeta wants to write the following user-defined functions:
Add\_Device(): To accept a record from the user and add it to the CSV file, Peripheral.csv.Count\_Device(): To count and display the number of peripheral devices whose price is less than 1000.Use csv.writer to write data to a CSV file and csv.reader to read data from a CSV file. Handle exceptions for invalid or header rows when processing numeric values.
The Add_Device() function:
Peripheral.csv in append mode.csv.writer().
The Count_Device() function:
Peripheral.csv in read mode.
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 \(P,O,Q\).