Lesson Plan #6



Lesson Plan #046

Class: PreCalculus Date: Wednesday January 8th, 2014

Topic: Ellipse Aim: What are some properties of ellipses?

Objectives:

1) Students will be able identify the different parts of an ellipse.

2) Students will be able to write the equation of an ellipse.

3) Students will be able to identify parts of an ellipse given its equation

HW# 046: Page 738 #’s 10, 14, 19, 22, 30, 32, 34, 38, 41, 48

Do Now:

Procedure:

Write the AIM and DO NOW

Get students working!

Take attendance

Give back work

Go over HW

Collect HW

What is an ellipse?

Standard equation for an ellipse:

Interactive Online Activity:

Area of an ellipse:

Sample Test Question:

1) 2)

3)

Eccentricity: Let’s explore

Sample Test Question:

1) Write an equation for the ellipse having foci at (–2, 0) and (2, 0) and eccentricity e = 3/4

2)

Sample Test Question

Latus Rectum:

In an ellipse, latus rectum length is

Assignment #1:

Find length of the latus rectum of the ellipse given by

[pic]

Assignment #2:

Find the length of the latus rectum of the ellipse given by

[pic]

Assignment #3:

If the length of the latus rectum of an ellipse is equal to one half the length of the minor axis, find the eccentricity of the ellipse.

Assignment #4:

Assignment #5:

Write the equation of the ellipse whose center is at the origin and passes through the points (-3,1) and (2,-2)

Another way to define an ellipse:

An ellipse is the locus of points whose distances to a fixed point (focus) and to a fixed line (directrix) are in a constant ratio (called the eccentricity) less than 1.

An ellipse is all points whose distance to the focus is equal to the eccentricity times the distance to the directrix.

From the picture e*PD=PF



The directrices are are given by equations or



Assignment #6:

Find the eccentricity of the ellipse with a focus at (3,0) and a vertex at (5,0). Find the area of the ellipse. Draw the latus recta of the ellipse. Find the length of the latus recta of the ellipse. Find the equations of the directricies of the ellipse. Draw in the directrices of the ellipse.

Applications:

Planetary Orbits:

Sample Test Questions:

1) A satellite is in an elliptical orbit with the center of Earth at one focus. The major axis of the orbit is 28,900 miles long and the center of the Earth is 8000 miles from the center of the ellipse. Assuming that the center of the ellipse is the origin and the foci lie on the x-axis, write the equation of the path of the satellite.

2) B.C. Place Stadium has an air-filled fabric dome roof that forms the shape of an ellipse when viewed from above. Its maximum length is approximately 230 m, its maximum width is approximately 190 m, and its maximum height is approximately 60 m.

A) Find an equation for the ellipse formed by the base of the roof.

Medicine:

The lithotripter machine has a half ellipsoid shaped piece that rests opening to the patient’s side. An ellipsoid is a three dimensional representation of an ellipse. In order for the lithotripter to work using the reflective property of the ellipse, the patient’s stone must be at one focus point of the ellipsoid and the shockwave generator at the other focus. The patient is laid on the table and moved into position next to the lithotripter. Doctors use a fluoroscopic x-ray system to maintain a visual of the stone. This allows for accurate positioning of the stone as a focus. Because the stone is acting as one of the focus points, it is imperative that the stone be at precisely the right distance from the focus located on the lithotripter. This is essential in order for the shockwaves to be directed onto the stone.



If Enough Time:

5) State the center, foci, vertices, and co-vertices of the ellipse with equation 25x2 + 4y2 + 100x – 40y + 100 = 0. Also state the lengths of the two axes

-----------------------

[pic]

Center

Vertices

Co Vertices

Foci

Eccentricity

Area

Length of latus recta

Equations of directricies

190 m

230 m

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