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8.1 8.1 Presentation Transcript

  • Conic Sectionsand ParabolasChapter 8.1
  • Chapter 8.1• The study of conic sections, or simply conics.• Conics are formed by the intersection of a planewith a pair of cones.
  • ParabolasAlgebraically speaking• y = ax2 + bx + c• Has a U-shape.• Opens with upward or downward.• The lowest or highest point on such a parabola iscalled the vertex.• It is symmetric about the its axis called the axis ofsymmetry.
  • Parabolas
  • Parabolas
  • Standard Form• The Standard Form of the equation of a parabolawith vertex at (h, k) is:• (x - h)2 = 4p (y- k), vertical axis; directrix at y = k - p• (y - k)2 = 4p(x - h), horizontal axis; directrix at x = h - p• The focus lies on the axis p units from the vertex.• Find the standard form of the equation of theparabola with vertex (2, 1) and focus (2, 4)
  • Standard Form
  • Standard Form• Find the standard form of the parabola with vertexat the origin and focus (2, 0)
  • Parabola