Chapter 4 - Rational Functions
and Conics
Algebra 3
Table of Contents
• 4.3 - Conics
• 4.4 - Translations of Conics
4.3 - Conics
Algebra 3
4.3
Section 4.3: Figure 4.18, Basic Conics
Do not copy
Section 4.3: Figure 4.19, Degenerate Conics
4.3
Copy into notes
• Parabola- is the set of all points
(x,y), in a plane that are
equidistant from a fixed line, the
directrix, and a fixed point, the
focus.
• The vertex is the midpoint
between the focus and the
directrix.
• The axis is the line through the
focus and perpendicular to the
directrix
Parabola Example
Also flashlights,
radar, satellites
4.3
Copy notes, do not copy pictures
• Standard Form with vertex at (0,0)
and directrix y = - p
– Is
– x2 = 4py,
• Standard Form with vertex at (0,0)
and directrix x = - p
– Is
p cannot equal 0
– Vertical Axis of Symmetry
– y2 = 4px ,
p cannot equal 0
– Horizontal Axis of Symmetry
4.3
Copy everything
• Ellipse- The set of all points (x,y) in a
plane with the sum of whose distances
from two distinct fixed points (foci) is
constant
• The midpoint between the foci is the
center. The line segment through the
foci, with major axis are the vertices.
• The line segment through the center
and perpendicular to the major axis,
with endpoints on the ellipse, is the
minor axis. The endpoints of the minor
axis are the covertices
4.3
Do not copy pictures
Major Axis has a length of 2a
Minor Axis has a length of 2b
c2 = a2 – b2 , to find foci
Ellipse “Equals
comes earlier”
A2 = b2 + c2
4.3
Copy Defintions
• Hyperbolas- a set of all the points (x,y) in
a plane where the difference of distances
from two distinct fixed points (foci “fosi”) is a positive constant
• The midpoint between the foci is the
center.
• The points at which the line segment
through the foci meets the hyperbola are
the vertices.
• The line segment joining the vertices is
the transverse axis
4.3
To find foci
c2 = a2 + b2
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Asymptotes: y = ±
x
To find foci
“Equal comes later
a2 + b2 = c2
Asymptotes: y = ±
Show box with vertices and asymptotes pg.361
x
To find foci for an Ellipse
C2 = a2 – b2 , to find foci
To find foci for a hyperbola
C2 = a2 + b2 or
“Equals comes earlier”
A2 = b2 + c2
“Equals comes later”A2 +b2 = c2
HW pg. 362
• 4.3 – 11-29 (Odd) Parabolas
– 35-51 (Odd) Ellipses
– 61-73 (Odd) Hyperbolas
4.4 - Translations of Conics
Alg 3
4.4
4.4
4.4
Sketch the graph of the
following conics
a) (x-1)2 + (y + 3)2 =9
b) (x+2)2 = 12(y-4)
c) (x-2)2 + (y+3) 2 =1
25
4
HW pg. 372
• 4.4– V 1-7:
– # 1-5 (Odd), 11-29 (Odd), 35-43 (Odd), 47, 57, 63,
89, 91