Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: G-GPE.A.1 · Level: Grade 10 Geometry
Problem 1 Write the Equation ★★★
A circular fountain is centered at (4, −5) on a park map and has a radius of 6 yards. Write the equation of its edge.
Problem 2 Centered at the Origin ★★★
A radar screen is centered at the origin. One range ring has radius 11 units. Write its equation.
Problem 3 Read Center and Radius ★★★
State the center and the radius of the circle (x + 2)² + (y + 8)² = 64.
Problem 4 Center on the x-Axis ★★★
A circle has center (−5, 0) and radius √10. Write its equation.
Problem 5 Equation from a Graph ★★★
Write the equation of the circle shown.
Problem 6 Radius from a Point ★★★
A circular skating rink is centered at (−3, 2) on a grid, and a light pole at (1, 7) stands exactly on its edge. Write the equation of the rink.
Problem 7 Equation from a Diameter ★★★
The endpoints of a diameter are (−4, 3) and (6, −1). Write the equation of the circle.
Problem 8 Inside, On or Outside ★★★
Circle C: (x − 1)² + (y + 2)² = 40. Decide whether each point is inside, on or outside: (a) (7, 0) (b) (−2, 3) (c) (5, 4).
Problem 9 Another Point on the Circle ★★★
A circle has center (−2, −4) and passes through (6, −1). Use the Pythagorean Theorem or the circle equation to show that (1, 4) is also on the circle.
Problem 10 Complete the Square: Basic ★★★
Rewrite x² + y² − 6x + 10y + 18 = 0 in standard form. Give the center and radius.
Problem 11 Complete the Square: Irrational Radius ★★★
Rewrite x² + y² + 8x − 2y − 4 = 0 in standard form. Give the center and the radius.
Problem 12 Completing the Square with Large Terms ★★★
Rewrite x² + y² − 12x − 4y + 20 = 0 in standard form. Give the center and the radius in simplest radical form.
Problem 13 Divide First ★★★
Rewrite 2x² + 2y² + 4x − 16y − 10 = 0 in standard form. Find the center and radius.
Problem 14 Circle, Point or Nothing? ★★★
Complete the square for each equation and say whether it is a circle, a single point or has no graph. (a) x² + y² − 4x + 6y + 13 = 0 (b) x² + y² − 4x + 6y + 20 = 0
Problem 15 Cell Tower Coverage ★★★
On a county map with 1 unit = 1 mile, a cell tower at (−3, 5) reaches 12 miles in every direction. (a) Write the equation of the edge of its coverage. (b) A town sits at (6, −3). Is it covered?
Problem 16 Flower Bed in a Corner ★★★
A circular flower bed with radius 4 feet fits in the corner formed by two perpendicular fences along the positive x-axis and y-axis, touching both fences. Write the equation of its edge.
Problem 17 Circle Through Three Points ★★★
A circular plaza passes through the points (0, 0), (10, 0) and (0, 4) on a city grid. Find the equation of the circle. (Hint: the angle at the origin is a right angle.)
Problem 18 Ferris Wheel Heights ★★★
A Ferris wheel has radius 10 feet and its center is 12 feet above the ground, directly above the origin of a coordinate system. (a) Write the equation of the wheel. (b) A rider is 5 feet to the right of the center line. How high above the ground can the rider be? Round to the nearest tenth.
Problem 19 Bike Path Through a Plaza ★★★
A circular plaza has equation (x − 1)² + (y − 2)² = 8 and a straight bike path follows y = x + 1. Find the two points where the path meets the edge of the plaza.
Problem 20 Tangent Line to a Circle ★★★
The point (3, 4) lies on the circle (x + 1)² + (y − 2)² = 20. (a) Verify this. (b) Find the equation of the tangent line to the circle at (3, 4).
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