Prepared by Mrs. Harlowat Douglas S. Freeman High School

Quiz Review

Applications of Conics

Think of a cone as beingdouble-napped.

• A. How is a circle cut?

• B. How can an ellipse be sliced?

• C. If you want a parabola, how do you slice the cone?

• D. To get both branches of a hyperbola, how is the cone cut?

After answering all questions

Good website: www.exploremath.com

• A. Circle• B. Ellipse• C. Parabola• D. Hyperbola

I remembered my conics definitions!

After reviewing all definitions

• SHAPE• A. Circle• B. Ellipse• C. Parabola• D. Hyperbola

• FEATURES• A. Equal distance from center• B. Total distance to foci

remains constant • C. All rays concentrate at focus• D. Rays are dispersed

Click each feature to see an example.

To finish

If you study, complete your various Review Sheets, and seek help, you

should do well on your test.

Just don’t plan to use that tired old excuse for not doing your homework.

If you are interested in reading more about this topic, go to Math Forum.

This space heater uses a parabolic reflector to focus heat. It feels much warmer than a similar heater (not parabolic) with less wattage.

The French Horn has a hyperbolic bell so that music is dispersed to all listeners. (After clicking on the French Horn, drag the note to hear the sound.)

For help with the definitions,

consult this math dictionary.

• Circle• Radius• Diameter• Center• Tangent

Master these terms.

Back

Does this movie remind you of the definition of ellipse?

What is the significance of the two blue lines moving around the ellipse?

If you still do not remember the definition, think about the ExploreLearning. What was the meaning of

1 2L L ?

Back to the question

Go to exploremath.com to refresh the definition of hyperbola.

Scroll down and check the box for “show string property,” move the blue dot around, and watch L1 L2 .

Back to the question

To help you remember the definition, click on the parabola.

Scroll down and check the box for “explore geometric definition,” move the blue dot around, and watch the values of 1 2L and L .

Back to the question

L1L1L1

A hyperbola is formed by slicing the cone perpendicular to the base (or really just not parallel to the slant height), cutting through both nappes to form the two branches.

What is a “degenerate hyperbola”?

Answer:

A “degenerate hyperbola” is a pair of intersecting lines.

An ellipse is sliced by a plane that is not parallel to the base, but does cut all the way through the cone.

Think: What is a “degenerate ellipse”?

Just like the circle, it is a point.

Answer:

A parabola is sliced parallel to one side, or, as you might have said in geometry, parallel to the slant height.

Think: What is a “degenerate parabola”?Hint: Keep the plane parallel to the slant height,

but slide it left until tangent to the cone. What

figure do you see at the plane of tangency?

Answer:

A “degenerate parabola” is a line.

To form a circle, the cone should be sliced parallel to the base.

Thinking question:

As you look at the circles getting smaller, what is the “circle” at the bottom of the cone called?

A “degenerate circle” is a point.

Answer:

PLANETARY ORBITS

For more information, ask Dr. Math.