### General Information

**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

### Test Item Specifications

**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 #:**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

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Task

## MFAS Formative Assessments

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

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

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.

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.

## Original Student Tutorials Mathematics - Grades 9-12

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

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

## Student Resources

## Original Student Tutorials

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

## Problem-Solving Task

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

Type: Problem-Solving Task

## Parent Resources

## Problem-Solving Task

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

Type: Problem-Solving Task