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.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations
Cluster: Level 2: Basic Application of Skills & Concepts
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
Assessed: Yes


  • Item Type(s): This benchmark may be assessed using: ETC item(s)

  • 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 :


  • 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

    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.


  • Test Item #: Sample Item 1
  • Question:

    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.

  • Difficulty: N/A
  • Type: ETC: Editing Task Choice