8.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{a911dc0b-351c-415c-a6df-2af652d5a59b-3_755_1024_934_322}
\end{figure}
The curve \(C\), shown in Fig. 1, represents the graph of \(y = \frac { x ^ { 2 } } { 25 } , x \geq 0\).
The points \(A\) and \(B\) on the curve \(C\) have \(x\)-coordinates 5 and 10 respectively.
- Write down the \(y\)-coordinates of \(A\) and \(B\).
- Find an equation of the tangent to \(C\) at \(A\).
The finite region \(R\) is enclosed by \(C\), the \(y\)-axis and the lines through \(A\) and \(B\) parallel to the \(x\)-axis.
- For points \(( x , y )\) on \(C\), express \(x\) in terms of \(y\).
- Use integration to find the area of \(R\).