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. \(x(t) = 2R\cos(t), y(t) = R\sin(t)\)
by
Geoff Pilling