1. Conic Sections - Ellipses
Chapter 8, Section 2

2. About Ellipses Definition Focus – one of the fixed points
The set of all points in a plane such that the sum of the distances from two fixed points is a constant.
Focus – one of the fixed points
Focal axis – the line through the foci
Center – the point on the focal axis midway between the foci
Vertex – endpoint of the major and minor axis

3. About Ellipses, continued…
Major axis:
Length is 2a
Is horizontal if x has the larger denominator
Is vertical if y has the larger denominator
minor axis:
Length is 2b
Focal radii – segment joining each focus to a point on the ellipse
Sum of lengths is 2a
Is the distance from the center to a focus

4. Horizontal Ellipses Center: (h,k) Focus: (h+c,k) (h-c,k)
Major axis: y=k
Major axis vertices: (h+a,k) (h-a,k)
Minor axis: x=h
Minor axis vertices: (h, k+b) (h, k-b)

5. Vertical Ellipses Center: (h,k) Focus: (h,k+c) (h,k-c) Major axis: x=h
Major axis vertices: (h,k+a) (h,k-a)
Minor axis: y=k
Minor axis vertices: (h+b,k) (h-b,k)

6. Examples – find the center, foci, vertices, major and minor axis

7. Examples – write the equation in standard form

8. Classwork/Exit Slip
Find the center, foci, vertices, major and minor axis:
Write the equation of the ellipse if the foci are at (-2,0) and (2,0) and a=7
Homework:
Page 652, #21, 24, 27, 33, 45, 46
Find vertices and foci on #45, 46