GOZUNTA
Try it now
Problem preview
G-GPE.1 Warmup M2-041-A03-V04

Derive the equation of a circle from center/radius and complete the square to identify center/radius.

Derive a circle equation from the distance formula

Problem

Let \((x,~y)\) be a point on the circle with center \((2,~5)\) and radius \(3\). Substitute the coordinate differences into the distance formula, square \(\text{both}~\text{sides}\), and simplify to the circle equation.

Coordinate plane with circle center (2,5), radius 3, and a general point (x,y); no equation is shown. Open full size
Inside Gozunta

Turn the preview into practice.

More than a preview

Gozunta lets you study this problem—and more than 10,000 others.

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now
Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-GPE.1
Category
Geometry
Domain
Expressing Geometric Properties with Equations
Objective
Derive the equation of a circle from center/radius and complete the square to identify center/radius.
Problem type
Derive a circle equation from the distance formula