Two Questions Name the Standard Conics

You'll learnto name the standard nonrotated conics from two quick questions about their equations.

Four curves, one family, and a classifier you can run in your head. Count the squared terms, then look at the sign between them. It works on the axis-aligned form used here — no xy term, and a real nondegenerate curve — which is where the exam meets these. Everything else — the centre, the radius, which way it opens — comes out of standard form, and standard form is reached by paying for the square you complete.

8 STEPS · 6 QUICK CHECKS · COUNT · SIGN · COMPLETE THE SQUARE · v3

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

the classifier runs left to right

Before you start

What you're looking at

Four graphs and four equations waiting to be matched, then a two-question classifier.

The question

How many squared terms are there, and what is the sign between them?

Watch for

Classification kept separate from completing the square — two different tasks. And the standing condition on the classifier: no xy term, and a real nondegenerate curve.

Step 1 / 8