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G-GPE.1 Warmup M2-041-A08-V04

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

Write a circle equation from its center and a point on the circle

Problem

A circle has center \((4,~-2)\) and passes through \((9,~10)\). Calculate the squared radius from the coordinate differences, write the center-radius equation, and verify the supplied point by substitution.

Coordinate plane showing center C at 4 comma negative 2 and point P at 9 comma 10 connected by an unlabeled segment. 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 its center and a point on the circle