12/7/2016
Lesson 6.4
SWBAT identify focus and
directrix.
SWBAT identify the properties of
sideways (horizontal opening)
parabolas
Agenda
•Do Now
•Lecture (From online text, 5-4)
•Guided Practice
•Independent Practice
•Exit Ticket
•Closing
12/7/2016
IV. Focus and Directrix of a Parabola
A. Focus and Directrix
1. Parabola is created by slicing a conic section (double cone)
2. Parabola is defined as all the set of points on a plane that are equidistant from a
fixed point and a fixed line
a) Focus –fixed point
b) Directrix – fixed line
B.
Properties
Focus
Directrix
Vertex Form
,
1
4
1
4
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Example 1: What is the equation of the parabola with vertex at origin and focus 0 2 ?
Example 2: What are the vertex, focus and directrix of the parabola with equation
1
2
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V. Properties of Sideways (Horizontal Opening Parabolas)
A. Equations of a sideways (horizontal opening parabola)
x h a y k or
1. Where does this come from?
B. Important properties
1. Vertex (h, k)  have to change signs on both
2. “a or ” value
• Open to right if a positive
• Opens to left if a negative
3. Focus
,
4. Directrix
C. Examples
1.
2
Direction of opening
5
Vertex
Axis of symmetry
Focus
Directrix
Direction of opening
2.
y
4
3
Vertex
Axis of symmetry
Focus
Directrix
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Example 3: Find the equation of sideways parabola with vertex 4, 2 and focus (8, 2)
VI. Relationship between Parabolas & Focus/Directrix
A. For a parabola that opens up:
• Directrix below the parabola &
Focus above
B. For a parabola that opens down:
• Directrix above parabola & Focus below
C. For a parabola that opens to the right:
• Directrix to the left of the parabola &
Focus to the right
D. For a parabola that opens to the left:
• Directrix to the right & Focus to the
left