Conic Sections and Parabolas

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Conic Sections and Parabolas

• 9.1-9.2

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Conic Sections

• Place two right circular cones together at their
  vertex. Now connect the centers of the bases
  with a line. Call this line the axis.

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Conic Sections

• Slice a cone perpendicular to the axis and you
  will get a circle.
• Slightly tilt the above plane and you will get an
  ellipse. The plane will not intersect the base
  of a cone.

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Conic Sections

• Tilt the plane further so that it intersects the
  base of the cone and a parabola will result.
• A plane that intersects the base of both cones
  will result in a hyperbola.

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Parabola

• A parabola is the set of all points equidistant
  from a particular line, called the directrix, and
  a particular point, called the focus, in the
  plane.

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Axis of Symmetry

• A line that passes through the focus and the
  vertex of the parabola. It is the line of
  symmetry for the parabola.

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Vertex

• The point where the parabola intersects its axis.
  This point is midway between the focus and the
  directrix.

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Parabola Facts

• Know the chart on page 658 of the book.
• Negative a means the parabola opens down or left.
• Positive a means the parabola opens up or right.
• X squared means the parabola opens up or down.
• y squared means the parabola opens left or right.

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Graphing on the Calculatory2

• Example (y-3)2 8(x2)
• Solve for y.
• Y1 will be 3 the square root
• Y2 will be 3 the square root

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Graphing on the Calculatorx2

• Example (x-3)2 8(y2)
• Solve for y.
• 8y 16 (x-3)2
• 8y -16 (x-3)2
• Y -2 (x-3)2/8
• Place result in y1

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Find the Equation of the Parabola Described

• 20,24,26,28

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Find the vertex, focus and directrix of each
parabola. Then graph by hand and by calc.

• Use the chart to help find the three items.
• When graphing, graph the three items and then
  graph two points on one side of the axis of
  symmetry and the two symmetric points on the
  other side.

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Write an Equation for a Parabola Given the vertex
and a point on the parabola.

• Find the correct standard form for the parabola
  based on how it points.
• Plug the vertex in for h and k.
• Plug the coordinate in for x and y.
• Solve for a.
• Write the equation with the a, h, and k plugged
  in, and leave the x and y as x and y.