Given:
Given the graph of an ellipse.
Required: Parametric form
Explanation:
The parametric form for an ellipse is F(t) = (x(t), y(t)), where x(t) = acos(t) + h and y(t) = bsin(t) + k.
From the graph, the center of the ellipse is (h, k) = (0, 0).
The length of the axes are 2a and 2b.
[tex]\begin{gathered} 2a=10\implies a=5 \\ 2b=6\implies b=3 \end{gathered}[/tex]
So, x(t) = 5cos(t) and y(t) = 3 sin(t).
Option C is correct.
Final Answer: x(t) = 5 cos(t) and y(t) = 3 sin(t)
