Conic Sections Part 2:Ellipses

Integrated Math 4

Mrs. Tyrpak

Ellipses

The parametric equations for ellipses:

What are the x-intercepts and y-intercepts of the ellipse?

Horizontal and Vertical Axes

What is the length of both axes in both Graphs?

Major and Minor Axes

The longer axis of an ellipse is the ________ axis, and the shorter is the

________ axis.

When will the horizontal axis of an ellipse be the major axis? The minor axis?___________________________

Eliminate the parameter

This will produce a rectangular equation for an ellipse.

Standard form for an Ellipse

Center (h,k)

Horizontal Axis: 2a

Vertical Axis: 2b

Using Standard Form

Write in standard form the equation of an ellipse with center (3, -5), horizontal axis length 12 and vertical axis length 20.

Write in expanded form

Expanded Form Standard

Write the following in standard form

and describe the nature of the graph.

You try one…

Write the following in standard form and describe the nature of the graph.

Secondary definition for an ellipse:

It is a set of points in a plane for which the sum of the distances from two fixed points, called the foci, is a constant.

General Case Explanation

Suppose the foci are , and that for any point P, the sum of the distances to the foci is 2a where

Explain the following:

1. Why the x-intercepts are (-a,0) and (a,0)

2. Why the y-intercepts are (0, -b) and (0, b), where

You know what I’m going to say!

Awesome job!!

Don’t forget to complete your extension and enrichment worksheets before you

move on.

Remember you are a mathematician