Parametric Equation Anyone?

Calculus Level 3

A parametric equation is a way of representing a relationship between two variables (say, \(x\) and \(y\)) by introducing a third variable, say \(t\), and setting up a set of equations as a function of this third variable.

Suppose we have the following equation of an ellipse:

\[x^2 + 4y^2 = R^2.\]

Which set of parametric equations will trace out a similar ellipse?

A. \(x(t) = R\cos(t), y(t) = \frac{R\sin(t)}{2}\)

B. \(x(t) = R\sin(t), y(t) = \frac{R\cos(t)}{2}\)

C. \(x(t) = R\cos(t), y(t) = 2R\sin(t)\)

D. \(x(t) = 2R\cos(t), y(t) = R\sin(t)\)


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