Conic Sections - Parabolas

1
Conic Sections - Parabolas

• Chapter 8, Section 1

2
About Parabolas

• Definition
• The set of all points in a plane equidistant from
  a given fixed line called the directrix and a
  given fixed point called the focus
• The distance from the focus to the vertex is the
  same as the distance from the vertex to the
  directrix
• The vertex is ½ the distance between the focus
  and the directrix
• Axis of symmetry is a line through the focus and
  vertex that is perpendicular to the directrix

3
About Parabolas, continued

• The vertex is the intersection of the axis of
  symmetry and the parabola
• is the distance from the focus to the
  vertex
• is the focal width of the parabola
• The length of a chord through the focus and is
  perpendicular to the axis

4
Horizontal Parabolas

• Vertex (h,k)
• Focus (hp,k)
• Axis of symmetry yk
• Directrix xh-p
• If pgt0, opens right
• If plt0, opens left

5
Vertical Parabolas

• Vertex (h,k)
• Focus (h, kp)
• Axis of symmetry xh
• Directrix yk-p
• If pgt0, opens up
• If plt0, opens down

6
General Form of parabolas
7
Examples find the vertex, focus, directrix,
axis of symmetry
8
Examples write the equation in standard form
9
Classwork/Exit Slip

• Find the vertex, focus, directrix, and axis of
  symmetry
• Write the equation in standard form
• Homework Page 639, 12, 15-20, 25, 26, 49-52