Parametric Equations

Curves traced by a parameter

Eliminating the parameter

Lines, circles, and ellipses

The cycloid and orientation

Which statement best captures what a parametric curve allows that a graph of a single function y = f(x) does not?

The curve is given by x(t) = t - 1 and y(t) = 2t + 4 for all real t. What is its equation in x and y?

Which pair of equations parametrizes the circle x squared plus y squared equals 16?

For x = cos t and y = sin t restricted to 0 at most t at most 2 pi, starting at the point (1, 0), how is the circle traversed?

For the cycloid x = r(t minus sin t) and y = r(1 minus cos t), what is the greatest height above the x axis?

Eliminating t from x = t squared and y = t on the interval from minus 1 to 2 gives y squared equals x. What curve is actually traced?

For the parametrization x(t) = 2t + 1 and y(t) = 3t - 4, what value of y corresponds to x = 5? Give a number.

The parametrization x = 3cos t and y = 3 sin t traces a circle. What is its radius? Give a number.

For x(t) = 4cos t and y(t) = 4 sin t, what is the value of x when t = pi? Give a number.

What one-word name is given to the direction in which a parametric curve is traced as the parameter increases?