Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for an equation of a circle quiz? Then this Geometry quiz on Writing and Graphing Circle Equations asks 10 multiple-choice questions with instant feedback. Ten multiple-choice questions on reading and writing circle equations, completing the square and locating points. Each explanation points out the sign or square-root slip behind the wrong choices.
Standards: G-GPE.A.1 · Level: Grade 10 Geometry
What this Writing and Graphing Circle Equations quiz checks
- Standard form: (x − h)² + (y − k)² = r², center (h, k), radius r.
- A circle centered at the origin is x² + y² = r².
- Complete the square in x and in y to read the center and radius from a general equation.
- A point is inside, on or outside the circle when its squared distance is less than, equal to or greater than r².
The 10 questions of the quiz
- What is the center of the circle (x − 5)² + (y + 2)² = 36?
- What is the radius of (x − 5)² + (y + 2)² = 36?
- Which equation describes the circle with center (0, 0) and radius 9?
- A circle has center (1, −3) and passes through (4, 1). What is r²?
- The point (5, 5) and the circle (x − 1)² + (y − 2)² = 20. Where is the point?
- What is its equation?
- To complete the square on x² + 14x, what number is added to both sides?
- What is the standard form of x² + y² − 4x = 5?
- The circle touches both axes. What is its equation?
- Which equation has no real graph?
After the quiz
Missed a question? Reread the Writing and Graphing Circle Equations lesson, then take the quiz again. Next, solve the Geometry worksheet on Writing and Graphing Circle Equations, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.