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Notes 8.1 Conics Sections

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Notes 8.1 Conics Sections The Parabola I. Introduction A.) A conic section is the intersection of a plane and a cone. B.) By changing the angle and the location ... – PowerPoint PPT presentation

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Title: Notes 8.1 Conics Sections


1
Notes 8.1 Conics Sections The Parabola
2
I. Introduction
  • A.) A conic section is the intersection of a
    plane and a cone.
  • B.) By changing the angle and the location of
    intersection, a parabola, ellipse, hyperbola,
    circle, point, line, or a pair of intersecting
    lines is produced.

3
  • C.) Standard Conics
  • 1.) Parabola
  • 2.) Ellipse
  • 3.) Hyperbola

4
  • D.) Degenerate Conics
  • 1.) Circle
  • 2.) Point
  • 3.) Line
  • 4.) Intersecting Lines

5
  • E.) Forming a Parabola
  • When a plane intersects a double-napped cone and
    is parallel to the side of the cone, a parabola
    is formed.

6
F.) General Form Equation for All Conics

If both B and C 0, or A and B 0, the conic is
a parabola
7
II. The Parabola
A.) In general - A parabola is the graph of a
quadratic equation, or any equation in the form
of
8
B.) Def. - A PARABOLA is the set of all points in
a plane equidistant from a particular line (the
DIRECTRIX) and a particular point (the FOCUS) in
the plane.
9
Axis of Symmetry
Focus
Focal Width
Vertex
Focal Length
Directrix
10
C.) Parabolas (Vertex (0,0))






Standard Form
Focus
Directrix
Axis of Symmetry
Focal Length
Focal Width
11
D.) Ex. 1- Find the focus, directrix, and focal
width of the parabola y 2x2.
Focus
Directrix
Focal Width
12
E.) Ex. 2- Do the same for the parabola
Focus
Directrix
Focal Width
13
F.) Ex. 3- Find the equation of a parabola with a
directrix of x -3 and a focus of (3, 0).
14
G.) Parabolas (Vertex (h, k))






St. Fm.
Focus
Directrix
Ax. of Sym.
Fo. Lgth.
Fo. Wth.
15
H.) Ex. 4- Find the standard form equation for
the parabola with a vertex of (4, 7) and a focus
of (4, 3).
16
I.) Ex. 5- Find the vertex, focus, and directrix
of the parabola 0 x2 2x 3y 5.
focus
Directrix
vertex
17
III. Paraboloids of Revolution
A.) A PARABOLOID is a 3-dimensional solids
created by revolving a parabola about an axis.
Examples of these include headlights,
flashlights, microphones, and satellites.
18
  • B.) Ex. 6 A searchlight is in the shape of a
    paraboloid of revolution. If the light is 2 feet
    across and 1 ½ feet deep, where should the bulb
    be placed to maximize the amount of light
    emitted?

19
The bulb should be placed 2 from the vertex of
the paraboloid
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