Question

Use the graph to answer the question.Which set of parametric equations represents the graph of the function shown?

Answer 1

Given:

Given the graph of an ellipse.

Required: Parametric form

Step-by-step 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.

`\begin{gathered} 2a=10\implies a=5 \\ 2b=6\implies b=3 \end{gathered}`

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)