Lesson 1:

What is a Conic?

By Carly Coffman

Open a Microsoft Word document and throughout the unit you will be asked to record insights, formulas, and observations on conics.  First, I want you to label the Word document with the title “Conics” and type your first and last name and period under the title.  Now, in the Word document type what you think a conic is or might be.  Take a guess if you have never heard of it.

Click on the following link to begin your exploration of conics:      Conic Occurence

Now, open your Word document and record the answers to the following questions in complete sentences.

1)        Name some of the mathematicians that first studied conics.

2)        What are the three types of conics listed on this webpage?

3)        Give two examples of applications of each type of conic that are found in the world around us.

Let’s now explore the double helix cone that provides us with each conic.  Look at each link below.  You can move the cone around by clicking the mouse on the cone and dragging it around.

(Open the links with Graphing Calculator, also known as NuCalc)

*You can change the width of the cone by adjusting the value of a.

Hyperbola

There are also special cases, which we call degenerate cases.  Explore the link and then answer each question in your Word document (in complete sentences).

1)        What will the intersection of the figures in this exploration form?

2)        What will the intersection of the figures in this exploration form?

3)        What will the intersection of the figures in this exploration form?

Next, search the internet for any places (that you did not list for question #3) where conics are found.  Find at least three more examples and explain each one.  Feel free to include pictures with your write-up.

On your word document explain in your own words what a conic is.  Mentally, compare this with your first description of a conic.  Was your initial definition / guess correct?

Once you are finished, double check to make sure your name is on your Word document.  Print this document and keep it in your notebook.  You will create documents throughout the unit and at the end of the unit I will assess these documents in a portfolio you create with them.