Circle Equations & Completing the Square
The Digital SAT frequently tests the standard form of a circle (x - h)² + (y - k)² = r² where (h, k) is the center and r is the radius. When given in expanded polynomial form x² + y² + Ax + By + C = 0, you must complete the square for both x and y to find the center or radius.
Core Formula & Concept Cheat Sheet
Desmos Speed-Run Trick
Type the exact expanded equation directly into Desmos (e.g., x^2 + y^2 - 6x + 8y = 24). Desmos will plot the circle immediately. Click the center or measure distance from center to edge to read radius instantly!
The 700+ Score Trap
Forgetting to take the square root of the right side (picking r² instead of r), or forgetting to flip signs when extracting center (h, k) from (x - h) and (y - k).
Test Your Mastery
Official Exam FormatLive Interactive Practice Drill
Frequently Asked Questions
How do you find the radius when the equation has coefficients in front of x² and y²?
First divide the entire equation by the leading coefficient so that x² and y² have a coefficient of 1 before completing the square.
Can I always use Desmos on Digital SAT circle questions?
Yes! Desmos is built into every Digital SAT Math module. You can graph any circle equation implicitly without rearranging.