Eliminating and introducing a parameter

Practice eliminating a parameter and constructing parametric equations for line segments, circles and simple algebraic curves. These precalculus questions emphasize a complete description: the Cartesian relation, inherited coordinate restrictions and direction of traversal.

Start with direct substitution, then work through exponential and trigonometric parameterizations, branch restrictions and counterexamples caused by squaring or dividing. Single-select and multiselect items include detailed worked explanations and checks against the original equations. Use algebra and standard trigonometric identities; no derivatives are needed. Write a candidate relation and its domain before comparing the choices.