CONIC
SECTIONS:
HYPERBOLAS
HONORS PRECALCULUS
1
MR. VELAZQUEZ
2
DEFINITION OF A
HYPERBOLA
3
HYPERBOLIC EQUATION
IN STANDARD FORM
HYPERBOLIC EQUATION
IN STANDARD FORM
y





b
c

x



(-c,0)





a



(c,0)







Using the Pythagorean theorem you can see that the relationship

4
is a 2  b2  c2
HYPERBOLIC EQUATION
IN STANDARD FORM
For the following equations is the transverse axis on
the x-axis or the y-axis?
y 2 x2
 1
4 5
5
x2 y 2

1
9 7
6
HYPERBOLIC EQUATION
IN STANDARD FORM
7
HYPERBOLIC EQUATION
IN STANDARD FORM
HYPERBOLIC EQUATION
IN STANDARD FORM
Find the vertices and locate the foci for
8
x2 y 2
the equation

 1.
36 13
HYPERBOLIC EQUATION
IN STANDARD FORM
Find the vertices and locate the foci for
9
x2 y 2
the equation.

1
16 9
HYPERBOLIC EQUATION
IN STANDARD FORM
10
Find the standard form of the equation of a hyperbola given
the following information: Foci (-4,0), (4,0) and vertices
(-3,0), (3,0)
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ASYMPTOTES OF
HYPERBOLAS
ASYMPTOTES OF
HYPERBOLAS
Find the asymptotes for the given hyperbola.
12
x2 y 2

1
4 12
ASYMPTOTES OF
HYPERBOLAS
Find the asymptotes for the given hyperbola.
13
y 2 x2
  1.
4 9
14
GRAPHING
HYPERBOLAS
GRAPHING
HYPERBOLAS
x2 y 2
Locate the vertices and foci for the equation

 1.
49 15
Draw the asymptotes and use them to graph the hyperbola.

y







         

x









 







15

GRAPHING
HYPERBOLAS
y 2 x2
Locate the vertices and foci for the equation
  1.
9 7
Then draw the asymptotes and use them to graph the hyperbola.

y







         

x









 







16

17
TRANSLATIONS OF
HYPERBOLAS
GRAPHING
HYPERBOLAS
Graph the equation of the hyperbola. Use the asymptotes
to draw the graph. Locate the center, vertices and foci.

y







         

x









 








18
( x  3)2 ( y  2) 2

1
1
3
GRAPHING
HYPERBOLAS
y



Write the standard form of the equation
of the hyperbola given the graph.


















19

COMPLETING THE
SQUARE (HYPERBOLAS)
20
Rewrite in standard form:
EXIT TICKET:
HYPERBOLAS
Find and graph the equation of the hyperbola
given the following information about it: the center
is (3, 1), the foci are (3, 4) and (3, −2), and the
vertices are (3, 2) and (3, 0).
NO HOMEWORK ASSIGNMENT FOR
THIS CHAPTER!!
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(HAVE A NICE WEEKEND)