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8.1 circles.ppt worked

Circles

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8.1 circles.ppt worked

  1. 1. Warm-up
  2. 2. What do we need to keep the same?
  3. 3. What do we need to change?
  4. 4. Chapter 8 Conic Sections “Circles”
  5. 5. What do you need to graph a circle?  Center (h, k)  Radius = r  Standard form of a circle:  (x - h)2 + (y - k)2 = r2
  6. 6. Examples  Ex: x2 + y2 = 25  Center (0, 0) Radius = 5  Ex: (x-2)2 + (y+4)2 = 49  Center (2, -4) Radius = 7
  7. 7. State the center and the radius for each:  (x + 4)2 + (y - 6)2 = 36  (x + 1)2 + (y - 3)2 = 49  (x + 3)2 + (y + 90)2 = 50  (x + 37)2 + (y - 12)2 = 50
  8. 8. State the center and the radius  x2 + 2x + 1 + y2 = 4  x2 + y2 – 4y – 16 = 0  x2 – 4x + 5 + y2 + 2y = 25
  9. 9. Graphing Circles  x2 + y2 = 25  (x-2)2 + (y+4)2 = 49
  10. 10. Now you graph these on your own!  (x - 3)2 + (y - 1)2 = 9  (x - 5)2 + (y - 4)2 = 16
  11. 11. Graph on your own…  (x - 1)2 + (y - 5)2 = 25  (x + 2)2 + (y - 7)2 = 36
  12. 12. Keep going!  (x + 7)2 + (y + 5)2 = 49  (x + 8)2 + (y + 10)2 = 50
  13. 13. Write the equation of the circle  Center (-4, 3) radius = 4  Center (5, -2) radius = 8  Center (-2, 3) radius = 3
  14. 14. Write the equation of the circle  For the translation of x2 + y2 = 9 four units left and three units up.  For the translation of x2 + y2 = 1 five units left and three units down.  For the translation of x2 + y2 = 4 two units right and seven units up.
  15. 15. Homework!  Worksheet

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