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