# Parametric Equation Anyone?

Calculus Level 2

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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