Practice Parametric Equations in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A way of defining a curve by expressing both x and y as separate functions of a third variable (parameter), typically t: x = f(t), y = g(t).
Instead of saying 'y depends on x,' parametric equations say 'both x and y depend on time t.' Imagine an ant walking on a table—at each moment t, the ant has an x-position and a y-position. The path it traces is the parametric curve, and t is the clock ticking forward.
Example 1
easyEliminate the parameter from x = 2t + 1 and y = t - 3 to find the rectangular equation.
Example 2
mediumEliminate the parameter from x = 3\cos(t) and y = 3\sin(t).
Example 3
mediumFind parametric equations for the line through (1, 4) and (5, -2).
Example 4
hardEliminate the parameter from x = t^2 - 1 and y = t^3 - t and describe the curve.