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G-GPE.1 Warmup M2-041-A07-V02

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

Write a circle equation from the endpoints of a diameter

Problem

A circle has diameter endpoints \((-2,~5)\) and \((4,~5)\). Find the midpoint for the center, calculate the diameter and radius, then write the center-radius equation.

Coordinate plane with diameter endpoints (−2,5) and (4,5) connected; center, radius, and circle equation are not shown. Open full size
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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
Write a circle equation from the endpoints of a diameter