Use the parametric equations of an ellipse
\[
\begin{array}{l}
x=12 \cos \theta \\
y=17 \sin \theta \\
0 \leq \theta \leq 2 \pi
\end{array}
\]
to find the area that it encloses.
Answer
Final Answer: The area that the ellipse encloses is \(\boxed{640.88}\).
Step 1 ：Given the parametric equations of an ellipse: \(x=12 \cos \theta\), \(y=17 \sin \theta\), where \(0 \leq \theta \leq 2 \pi\).
Step 2 ：The area of an ellipse is given by the formula \(\pi ab\), where \(a\) and \(b\) are the semi-major and semi-minor axes respectively.
Step 3 ：In this case, \(a=12\) and \(b=17\).
Step 4 ：Substitute these values into the formula to find the area: \(\pi \times 12 \times 17\).
Step 5 ：Calculate the area to get approximately 640.8849013323178.
Step 6 ：Final Answer: The area that the ellipse encloses is \(\boxed{640.88}\).
