Study Guide

Circle Equations and Measurements

Connect a circle’s graph, equation and measurements. In (x − h)² + (y − k)² = r², the center is (h, k), and r is the radius.

Key Rules

Read the center from the subtracted coordinates, paying attention to signs.
Take the square root of the right-hand side to find the radius.
Use circumference 2πr and area πr² when the question asks for measurements.

Common Mistakes to Avoid

Reporting r² as the radius.
Confusing the radius with the diameter, which is twice as large.

SAT Strategy Tips

→Rewrite plus signs as subtraction of a negative before reading a center.
→Substitute a known point to check whether it lies on the circle.

Example Question

A circle has equation (x − 2)² + (y + 3)² = 25. What are its center and radius?

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