1. Today’s Date: 2/5/14 www.Mathopenref.com 9.4 Ellipses

2. Making the Ellipse Get in groups of 3 Each person should have a piece of string & 2 pieces of tape Choose a point to plot on the x-axis Each person should choose a different point - One choose a point further from origin - One choose a point closer to origin

3. Making the Ellipse Make the origin the midpoint and plot a second point on the x-axis If I choose 3 as my 1 st point, my 2 nd point would be -3 Label these points as F 1 and F 2 Tape one end of the string to F 1 and the other end of the string to F 2 Place a PENCIL against the string and keep the string taut while moving the pencil around. F1F1 F2F2

4. Making the Ellipse What type of shape did you make? Compare your shape to the other shapes in your group. How are they similar? different? The further away the points are from the origin, the more elongated the ellipse will be. We call that ECCENTRICITY. How did the placement of your points affect your shape?

5. Definition of an Ellipse The set of all points P in the plane such that the sum of the distances from P to two fixed points is a given constant.

6. Vocabulary 1)F 1 and F 2 are called ________(singular: focus). 2)The midpoint of the segment F 1 F 2 joining the foci is the _________ of the ellipse. 3)The line segment passing through the foci is called the ____________ axis. 4)The segment through the center of the ellipse perpendicular to the major axis is the __________ axis. 5)The foci are always on the _____________ axis. foci center major minor major

7. Vocabulary 6)The length of the major axis is _________. The length of the minor axis is _________. 7)The sum of the focal radii is _____. (string = 2a) 8)Eccentricity is a measure of the shape of the ellipse. E = _______. (Closer the ratio is to 1, more elongated) 2a 2b 2a (a, 0) (-a, 0) (0, b) (0, -b) (-c, 0) (c, 0) P

8. Equations in Standard Form of ellipses centered at (0, 0) Major axis is on the x-axis:Major axis is on the y-axis: The foci are c units from center where: b a a b a 2 is the bigger # “C A B”

9. Example 1) Draw the ellipse given by: a = b = Foci: 53 ( 4, 0 ) and ( - 4, 0 ) on x- axison y- axis on x- axis Eccentricity =

10. Example 3) Draw the ellipse given by: a = b = Foci: 62 on y- axison x- axis on y- axis Eccentricity =

11. Homework #912 Page 421 #1-21 odd