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8.2 ellipses.ppt worked

Ellipses

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8.2 ellipses.ppt worked

  1. 1. Warm-Up  Range Graphically (#9 on CQ#1)
  2. 2. Homework Questions
  3. 3. Chapter 8 Ellipses
  4. 4. Ellipses  Standard Form of an Ellipse  Center (h, k)  a is your hm (horizontal movement)  b is your vm (vertical movement) 1 )()( 2 2 2 2 = − + − b ky a hx
  5. 5. Graph (and state vertices and co-vertices…major and minor axis) 1 8149 22 =+ yx
  6. 6. Graph 1 2536 22 =+ yx
  7. 7. Graph 1 9 )2( 64 )3( 22 = + + − yx
  8. 8. Graph 164 22 =+ yx 225925 22 =+ yx
  9. 9. Write an equation of an ellipse. 1. Center at the origin and vertex at (0,5) and co-vertex at (2,0) 2. Center at the origin and vertex at (0,-6) and co-vertex at (3,0) 3. Find an equation of an ellipse centered at the origin that is 12 units wide and 30 units high.
  10. 10. Additional Examples: 1. Write an equation in standard form of an ellipse that has a vertex at (0,-4), a co-vertex at (3,0) and is centered at the origin. 2. Find an equations of an ellipse centered at the origin that is 20 units wide and 10 units high.
  11. 11. Write the equation of a translated Ellipse 1. Write an equation of an ellipse with center (-3,-2), vertical major axis of length 8 and minor axis of length 6. 2. Write an equation of an ellipse with center (1,-4), horizontal major axis of length 10, and minor axis of length 4.
  12. 12. Write in Standard Form: 1. 25x²+16y²+150x = 160y-225 2. 2x²+8x+y²+4 = 0
  13. 13. Now you try…Write in standard form. 1. 4x²+y² - 24x + 6y + 9 = 0 1. x² + y² - 12x+ 4y = 8
  14. 14. Add in Focus!!
  15. 15. Let’s look at #3 on your worksheet…or others with foci
  16. 16. Homework Worksheet Quiz tomorrow on Circles and Ellipses!

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