This is a model of conic slices that is obtained through reverse-engineering parts of a cone, with its dimensions determined by its isosceles triangular frame and the angle of the cross-sectional slices.

**Big Idea**

Conic sections

**Purpose**

To explore conic sections, which are the cross-sections of a cone that include circles, ellipses, parabolas, and hyperbolas

**Sample Tasks and Explorations:**

- Using the conic sections model, find the measures of the angles that each conic section makes with the base of the cone.
- Suppose the base angles of the isosceles triangular frame of a cone measure 30 degrees. What kind of conic section is formed when a cross-section is formed at an angle of:

90 degrees from the horizontal base?

60 degrees from the horizontal base?

30 degrees from the horizontal base?

15 degrees from the horizontal base?

0.00000001 degrees from the horizontal base? - A circle is formed by cutting a cross section of a cone parallel to its base. Use the model to describe the kinds of cuts that produce an ellipse.
- What is the difference between the kinds of cuts that produce a circle and the kinds of cuts that produce a hyperbola?
- What is the difference between the kinds of cuts that produce an ellipse and the kinds of cuts that produce a parabola?