Conics as a Locus of Points

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Middle Grades Math: Geometry

Math: PreAlgebra: Geometry

Level

6-8

Activity Time

90 Minutes

Software

TI Connect™

TI Calculator

TI-83 Plus Family

TI-84 Plus

TI-84 Plus Silver Edition

Applications

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Other Materials

TI-Presenter™

LCD Projector
Two screens

Resource Types

Lessons

Report an Issue

Conics as a Locus of Points

Activity Overview

Students investigate the definition of a parabola through one of its geometric definitions. They study conic sections. They examine an ellipse as a locus of points such that the sum of distances from the foci to the traced path is constant.

Before the Activity

Install the Cabri Jr.™ App on the students' graphing calculators using one of these two methods:

TI-Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable

TI-Navigator™ "send to class" feature

See the attached PDF file for detailed instructions for this activity

Print pages 1 - 6 from the attached PDF file for your class

During the Activity

Distribute the pages to your class.

Follow the Activity procedures:

Exploration 1:

Draw a segment to connect a line (directrix) with a point (focus) not on it

Construct a perpendicular to the directrix at the point D where the segment intersects it

Construct a perpendicular bisector of the original segment

Mark Point P as the point of intersection of the two perpendiculars

Draw a circle using P as center P passing through the focus

Drag point D along the directrix

Observe that the path traced by point P is a parabola

Exploration 2:

Draw a circle

Draw a segment connecting a point A on the circle to a point B within the circle

Construct a perpendicular bisector of the segment

draw a line to connect the point A to the center of the circle

Label the point of intersection of the radius and the bisector as P

Drag the point A on the circle along the circumference

Observe that the path traced by P is an Ellipse

Drag point B outside the circle and observe the path traced is a hyperbola

Exploration 3:

Draw a circle and mark a point B outside the circle

Draw a second circle with a point on the first circle as its center, and passing through B

Drag the center of the second circle around the circumference of the first circle

Observe that the path traced by point B is a limacon with a loop when the point is outside the first circle, a limacon without a loop if it is inside the circle, and a cardioid if it is on the circle

After the Activity

Review student results:

As a class, discuss questions that appeared to be more challenging

Re-teach concepts as necessary

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Middle Grades Math: Geometry

Math: PreAlgebra: Geometry

Level

6-8

Activity Time

90 Minutes

Software

TI Connect™

TI Calculator

TI-83 Plus Family

TI-84 Plus

TI-84 Plus Silver Edition

Applications

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Other Materials

TI-Presenter™

LCD Projector
Two screens

Resource Types

Lessons

Report an Issue

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Conics as a Locus of Points

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Conics as a Locus of Points

Before the Activity Files

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

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