8.3

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8.3

  1. 1. Conic Sectionsand ParabolasChapter 8.1
  2. 2. Chapter 8.3• The study of conic sections, or simply conics.• Conics are formed by the intersection of a planewith a pair of cones.
  3. 3. HyperbolasGeometrically speaking• The set of all points in the plane, the differences ofwhose distances from two fixed points foci (plural offocus) is a constant.• The line through the foci is the focal axis.• The hyperbola consists of two parts called itsbranches,• The points where the hyperbola intersects its focalaxis are the vertices of the hyperbola.• Its center is halfway between the two vertices.
  4. 4. Hyperbola
  5. 5. Standard Form
  6. 6. Axes• A line segment with endpoints on a hyperbola is achord of the hyperbola.• The chord lying on the focal axis connecting thevertices is the transverse axis of the hyperbola.• The length is 2a.• The line segment of length 2b that is perpendicularto the focal axis and that has the center of thehyperbola as its midpoint is the conjugate axis ofthe hyperbola.• The number a is the semitransverse axis and b is thesemiconjugate axis.
  7. 7. Find the Equation• Find an equation of the hyperbola whose transverseaxis has endpoints (-2, -1) and (8, -1) and whoseconjugate axis length 8.
  8. 8. Find the Key Points

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