Standard #: MAFS.912.G-GPE.1.1 (Archived Standard)


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Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations
Cluster: Translate between the geometric description and the equation for a conic section. (Geometry - Additional Cluster) (Algebra 2 - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :
    In items where the student has to complete the square to find the
    center and radius of the circle, coefficients of quadratic terms should
    equal 1 and all other terms should have integral coefficients.
    Calculator :

    Neutral

    Clarification :
    Students will use the Pythagorean theorem, the coordinates of a
    circle’s center, and the circle’s radius to derive the equation of a
    circle.

    Students will determine the center and radius of a circle given its
    equation in general form. 

    Stimulus Attributes :
    Items may be set in a real-world or mathematical context.
    Response Attributes :
    Items may require the student to draw a circle that matches an
    equation in general form.



Sample Test Items (1)

Test Item # Question Difficulty Type
Sample Item 1

Johnny wants to find the equation of a circle with center (3,-4) and a radius of 7. He uses the argument shown.

There are three highlights in the argument to show missing words or phrases. For each highlight, click on the word of phrase that correctly fills the blank.

N/A ETC: Editing Task Choice


Related Courses

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1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1202340: Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1207310: Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1298310: Advanced Topics in Mathematics (formerly 129830A) (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))


Related Resources

Formative Assessments

Name Description
Complete the Square for Center-Radius 2

Students are asked to find the center and radius of a circle given its equation in general form.

Derive the Circle – General Points

Students are given the coordinates of the center, (h, k), and the radius, r, of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Derive the Circle – Specific Points

Students are given the coordinates of the center and the radius of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Complete the Square for Center-Radius

Students are asked to find the center and radius of a circle given its equation in general form.

Lesson Plans

Name Description
Circle Reasoning

Students use the Pythagorean Theorem (Distance Formula) to derive the Standard Equation of a Circle; then move between descriptions and equations of a circle.

Equations of Circles 1 This lesson unit is intended to help you assess how well students are able to use the Pythagorean theorem to derive the equation of a circle and translate between the geometric features of circles and their equations.
Equations of Circles 2 This lesson unit is intended to help you assess how well students are able to translate between the equations of circles and their geometric features and sketch a circle from its equation.
Run Fido, Run!

A guided practice for deriving the equation of a circle and then identifying a location to tether a dog to maximize movement.

Original Student Tutorials

Name Description
Where IS that Cell Tower?

Find the location and coverage area of cell towers to determine the center and radius of a circle given its equation, using a strategy completing the square in this interactive tutorial. 

Circle Up!

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions in this interactive tutorial.

Problem-Solving Task

Name Description
Slopes and Circles

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever ?AXB is a right angle

Student Resources

Original Student Tutorials

Name Description
Where IS that Cell Tower?:

Find the location and coverage area of cell towers to determine the center and radius of a circle given its equation, using a strategy completing the square in this interactive tutorial. 

Circle Up!:

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions in this interactive tutorial.

Problem-Solving Task

Name Description
Slopes and Circles:

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever ?AXB is a right angle



Parent Resources

Problem-Solving Task

Name Description
Slopes and Circles:

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever ?AXB is a right angle



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