Teaching Algebra with Manipulatives

Conic Sections
NAME ______________________________________________ DATE
Algebra Activity Recording Sheet
____________ PERIOD ____
(Use with the Lesson 8-6 Follow-Up Activity on pages 453–454 in the Student
Edition.)
Materials:
conic graph paper
Model and Analyze
1. Use the type of graph paper you used in Activity 1. Mark the
intersection of line 0 and circle 2. Then mark the two points on line 1
and circle 3, the two points on line 2 and circle 4, and so on. Draw the
new parabola. Continue this process and make as many parabolas as
you can on one sheet of the graph paper. The focus is always the center
of the small circle. Why are the resulting graphs parabolas?
2. In Activity 2, you drew an ellipse such that the sum of the distances
from two fixed points was 13. Choose 10, 11, 12, 14, and so on, for that
sum, and draw as many ellipses as you can on one piece of the graph
paper.
a. Why can you not start with 9 as the sum?
b. What happens as the sum increases? decreases?
3. In Activity 3, you drew a hyperbola such that the difference of the
distances from two fixed points was 7. Choose other numbers and draw
as many hyperbolas as you can on one piece of graph paper. What
happens as the difference increases? decreases?
© Glencoe/McGraw-Hill 270 Teaching Algebra with Manipulatives