10.1 Parabolas - PowerPoint PPT Presentation

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10.1 Parabolas

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If p is greater than zero, the parabola opens upward: y = 2x2 ... Find the equation of the parabola with focus (-1,0) and directrix x = 1: ... – PowerPoint PPT presentation

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Title: 10.1 Parabolas


1
10.1 Parabolas
  • A parabola is the set of all points that are
    equidistant from a fixed point (focus) and a
    fixed line (directrix).
  • y 1/(4p) x2
  • Where the vertex is the origin
  • the focus is at (0,p)
  • the directrix is the line y -p
  • If p is greater than zero, the parabola opens
    upward y 2x2
  • If p is less than zero, the parabola opens
    downward y -1/8 x2

2
  • The presence of h and k in the standard equation
    results in horizontal and vertical shifts
  • of the vertex to the point (h,k).
  • y 2 ¼ (x-1)2
  • x - 5 6 (y2)2
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