Intro to Conics - PowerPoint PPT Presentation

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Intro to Conics

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  1. Introduction to Conic Sections

  2. A conic section is a curve formed by the intersection of _________________________ a plane and a double cone.

  3. (h , k) r Circles The set of all points that are the same distance from the center. Standard Equation: With CENTER: (h, k) & RADIUS: r (square root)

  4. ® - h , ) ( 2 8 Example 1 -h r² -k Center: Radius: r 9 ( ) k ,

  5. Example 2 Center ? Radius ?

  6. Standard Equation: (h , k) a b Ellipse Basically an ellipse is a squishedcircle Center: (h , k) a: major radius (horizontal), length from center to edge of circle b: minor radius (vertical), length from center to top/bottom of circle * You must square root the denominator

  7. This must equal 1 a² b Example 3 2 Center: (-4 , 5) a: 5 b: 2

  8. Standard Equations: OR vertex Parabola vertex We’ve talked about this before… a U-shaped graph This equation opens left or right This equation opens up or down HOW DO YOU TELL…LOOK FOR THE SQUARED VARIABLE • Vertex: (h , k) • If there is a negative in front of the squared variable, then it opens down or left. • If there is NOT a negative, then it opens up or right.

  9. Example 5 Example 4 opens down What is the vertex? How does it open? (-2 , 5) opens right What is the vertex? How does it open? (0 , 2)

  10. Standard Equations: OR Hyperbolas What I look like…two parabolas, back to back. This equation opens up and down This equation opens left and right Have I seen this before? Sort of…only now we have a minus sign in the middle (h , k) Center: (h , k)

  11. Example 6 Center: (-4 , 5) Opens: Left and right

  12. What am I? Name the conic section and its center or vertex.

  13. circle; (0,0)

  14. hyperbola; (0,0)

  15. parabola; vertex (1,-2)

  16. parabola; vertex (-2,-3)

  17. circle; (2,0)

  18. ellipse; (0,0)

  19. hyperbola; (1,-2)

  20. circle; (-2,-1)

  21. hyperbola; (-5,7)

  22. parabola; vertex (0,0)

  23. hyperbola; (0,1)

  24. ellipse; (-5,4)