Standard 7: Apply geometric and algebraic representations of conic sections.

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General Information
Number: MA.912.GR.7
Title: Apply geometric and algebraic representations of conic sections.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Geometric Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.912.GR.7.AP.2
Create the equation of a circle when given the center and radius.
MA.912.GR.7.AP.3
Given an equation of a circle, identify center and radius, and graph the circle.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Formative Assessments

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.

Type: Formative Assessment

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.

Type: Formative Assessment

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.

Type: Formative Assessment

Complete the Square for Center-Radius:

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

Type: Formative Assessment

Lesson Plans

Space Equations:

In this lesson, students model the orbit of a satellite and the trajectory of a missile with a system of equations. They solve the equations both graphically and algebraically.

Type: Lesson Plan

I'm Focused on the Right Directrix:

In this lesson, the geometric definition of a parabola is introduced. Students will also learn how to write the equation of a parabola in vertex form given its focus and directrix.

Type: Lesson Plan

Discovering Properties of Parabolas by Comparing and Contrasting Parabolic Equations:

  • Teachers can use this resource to teach students how to derive the equation of a parabola in vertex form y = a(x – h)2 + k, when given the (x, y) coordinates of the focus and the linear equation of the directrix.
  • An additional interactive graphing spreadsheet can be used as a resource to aid teachers in providing examples.

Type: Lesson Plan

Acting Out A Parabola: the importance of a vertex and directrix:

Students will learn the significance of a parabola's vertex and directrix. They will learn the meaning of what exactly a parabola is by physically representing a parabola, vertex, and directrix. Students will be able to write an equation of a parabola given only a vertex and directrix.

Type: Lesson Plan

Explore the Properties of a Parabola and Practice Writing its Equation:

Students learn parabola properties, how to write parabola equations, and how to apply parabolas to solve problems.

Type: Lesson Plan

Ellipse Elements and Equations:

Students will write the equation of an ellipse given foci and directrices using graphic and analytic methods.

Type: Lesson Plan

Anatomy of a Parabola:

Students learn the parts of a parabola and write its equation given the focus and directrix. A graphic organizer is used for students to label all parts of the parabola and how it is created.

Type: Lesson Plan

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.

Type: Lesson Plan

The Math Behind the Records:

Students will develop an understanding of how the position of the focus and directrix affect the shape of a parabola. They will also learn how to write the equation of a parabola given the focus and directrix. Ultimately this will lead to students being able to write an equation to model the parabolic path an athlete's center of mass follows during the high jump.

Type: Lesson Plan

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.

Type: Lesson Plan

A Point and a Line to a Parabola!:

In this lesson, the student will use the definition of a parabola and a graphing grid (rectangular with circular grid imposed) to determine the graph of the parabola when given the directrix and focus. From this investigation, and using the standard form of the parabola, students will determine the equation of the parabola.

Type: Lesson Plan

Introduction to the Conic Section Parabola:

This lesson is an introduction into conic sections using Styrofoam cups and then taking a closer look at the parabola by using patty paper to show students how a parabola is formed by a focus and a directrix.

Type: Lesson Plan

Original Student Tutorials

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. 

Type: Original Student 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.

Type: Original Student Tutorial

Perspectives Video: Teaching Idea

Representations of Parabolic Functions:

Don't get bent out of shape! Here's some ideas about how parabolic functions are connected to the real world and different ways they can be represented.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

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 angle AXB is a right angle.

Type: Problem-Solving Task

Triangles inscribed in a circle:

This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.

Type: Problem-Solving Task

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorials

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. 

Type: Original Student 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.

Type: Original Student Tutorial

Problem-Solving Tasks

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 angle AXB is a right angle.

Type: Problem-Solving Task

Triangles inscribed in a circle:

This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Problem-Solving Tasks

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 angle AXB is a right angle.

Type: Problem-Solving Task

Triangles inscribed in a circle:

This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.

Type: Problem-Solving Task