Turning a Curve Into a Trip

You'll learnto turn a curve's equation into an ordered trip around it.

An implicit equation states a condition and stops there: it says which points belong, never in what order to visit them. A parametrization supplies the missing itinerary. Building one is guesswork until you verify it by substitution, and verifying it is only half the job, because a parametrization can be correct and still cover the wrong piece.

8 STEPS · 6 QUICK CHECKS · BUILD · SUBSTITUTE · AUDIT THE COVERAGE · v2

Unit 4 is not assessed on the AP exam; schools include it where local requirements ask.

arrowheads show the direction of travel

Before you start

What you're looking at

The same circle shown two ways: unordered points that satisfy an equation, and an ordered point traveling it.

The question

What does a parametrization add that the bare equation does not?

Watch for

Two separate checks: every generated point satisfies the equation, and the interval covers the intended piece.

Step 1 / 8