March 27th copyright2009merrydavidson

HYPERBOLA’S• A hyperbola looks sort of like two

mirrored parabolas.• The two "halves" being called

"branches". • A hyperbola has two foci and two

vertices.• Hyperbola’s also have asymptotes.

HYPERBOLA’SDefinition:

The set of all points for which the difference in the distance to two fixed points (called the foci) is constant.

Horizontal Hyperbola

d2

d1

d1-d2= constant

Horizontal Hyperbola

d2d1

d1-d2= constant

Horizontal Hyperbola

d2d1

d1-d2= constant

Horizontal Hyperbola

c = center to focus

b = center to boxa = center to vertex

“x” term is positive

Major/Transverse axis goes through vertices.

Minor/Conjugate axis

ab

c

asymptote

HORIZONTAL hyperbola

Vertical Hyperbola

c = center to focusb = center to box

a = center to vertex

“y” term is positive

Major/Transverse axis goes through vertices.

Minor/Conjugate axis b

a

c

asymptote

Vertical Hyperbola

Horizontal Hyperbola Vertical Hyperbola

c2 = a2 + b2

SUMMARY

MAJOR axis does NOT mean longer.

Ex 1:Horizontal/Vertical? Center:a2= a=

b2= b= 

c 

19)3(

25)1( 22

yx

(-1,3)25 5

9 3 c2 = a2 + b2

2 25 9c

34 5.8c 5.8

Let’s draw what we know so far…

Draw in the box.

Ex 1: 19)3(

25)1( 22

yx

Draw in the asymptotes.Draw in the branches.

Place “c” on the graph.F1: F2: ( 1 34,3) ( 1 34,3)

Ex 2:

Horizontal/Vertical? Center:

a2= a=

b2= b= c = 

2 24( 1) 25 100y x

(0,1)

25 5

4 2

c2 = a2 + b2

2 25 4c 29 5.4c 5.4

Let’s draw what we know so far…

2 2( 1) 125 4y x

Insert a “4” on your notes!

Draw in the box.

Ex 2:

Draw in the asymptotes.Draw in the branches.

Place “c” on the graph.F1: F2:

2 2( 1) 125 4y x

(0,1 29) (0,1 29)

Ex 3: Find the center, foci, and the equation of the asymptotes.

2 22 21

4 16x y

Center:Major axis: horizontal or vertical

a = Verticesb =c = Foci

4x2 – y2 - 16x - 4y -4 = 0

(2,-2)

24

(4,-2),(0,-2)

(4 2 5)20 2 5

Ex 4: Find the equation of the hyperbola if the vertices are at (5,0) and (-5,0) and b2 = 49.

Draw in what you know.

Where is the vertex?(0,0)

Major axis: H or V?

Fill in the equation.2 2

125 49x y

Ex 5.

Write the equation for the hyperbola graphed on your notes.

HW: WS 10-5