Parametric Equation Anyone?

Calculus Level 2

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

Suppose we have the following equation of an ellipse:

x2+4y2=R2.x^2 + 4y^2 = R^2.

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

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

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

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

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

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