0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# 10.4 ellipses

332

Published on

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
332
On Slideshare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
15
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. Definition of an Ellipse Set of all points P such that the sum of thedistances between P and the two foci (pluralfor “focus”) is constant.d1 + d2 = constant
• 2. Characteristics of Ellipses
• 3. Standard form Ellipse Equation: a > b > 0The foci are on the major axis, c units from thecenter, where c2 = a2 – b2Equation Major Axis Vertices Co-VerticesHorizontal ( a, 0) (0, b)Vertical (0, a) ( b, 0)
• 4. Graphing1. Write in standard form.2. Use a and b to plot vertices and co-vertices.3. Draw the ellipse connecting all 4 points.Example:Draw the ellipse given byand identify the foci.
• 5. Your Turn! Graph and identify the foci.
• 6. Writing Equations Write an equation of the ellipse with the givencharacteristics and center (0, 0). Vertex: (0, 7)Co-Vertex: (-6, 0) Vertex: (-4, 0)Focus: (2, 0)
• 7. Your Turn! Write an equation of the ellipse with center(0,0) and: vertex at (3, 0) co-vertex at (0, -1)
• 8. Area of an Ellipse A = πabExample:A portion of the White House lawn is called TheEllipse. It is 1060 feet long and 890 feet wide.1. Write an equation of The Ellipse.2. Find the area of The Ellipse.
• 9. Modeling with an Ellipse In it’s elliptical orbit, Mercury ranges from46.04 million km to 69.86 million km from thecenter of the sun, which is a focus of theorbit. Write an equation of the orbit.