9 The curve in Fig. 9.1 has equation \(\sqrt { x } + \sqrt { y } = 1\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2f403099-2813-40d8-a9ae-1f7e64d41f80-4_426_647_299_667}
\captionsetup{labelformat=empty}
\caption{Fig. 9.1}
\end{figure}
- Show that this is part, but not all of the curve \(y = 1 - 2 \sqrt { x } + x\).
Sketch the full curve \(y = 1 - 2 \sqrt { x } + x\).
- Fig.9.2 shows a star shape made up of four parts, one of which is given in part (i) above.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2f403099-2813-40d8-a9ae-1f7e64d41f80-4_380_681_1197_651}
\captionsetup{labelformat=empty}
\caption{Fig. 9.2}
\end{figure}
For each of the sections of the shape labelled \(\mathrm { A } , \mathrm { B }\) and C , state the equation of the curve and the domain. - The shape shown in Fig.9.2 is made into that in Fig. 10.3 by stretching the part of the figure for which \(y > 0\) by a scale factor of 2 .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2f403099-2813-40d8-a9ae-1f7e64d41f80-4_405_686_1996_605}
\captionsetup{labelformat=empty}
\caption{Fig. 9.3}
\end{figure}
Find the area of this shape.