Hyperbolas T

Aim: How do we graph, recognize, andwrite the equation of a hyperbola?

MB4310/22/08Lomas

HW: Read 528-532Do 532-3 #3-6,8Do Now:

Circle or Ellipse? How can you tell?

HW Review: 6, 8

4x2 + 9y2 = 36

2x2 + 2y2 = 8

2x2 - 2y2 = 32


MB4310/22/08Lomas

HW: Read 528-532Do 532-3 #3-6,8px2 + qy2 = s

Is a hyperbola when p and q have different signs

Just like ellipses, we want to get hyperbolas in the form:

OR x2 y2

a2 b2+ = 1-

And it's done the same way

x2 y2

a2 b2- = 1


MB4310/22/08Lomas

HW: Read 528-532Do 532-3 #3-6,8

Hyperbola's only have one set of intersects, because they only touch one set of axes

We can tell which axis the intercepts are on by looking at the signs of p and q (or a2 and b2). Whichever one has the same sign as s will have the intercepts.


MB4310/22/08Lomas

HW: Read 528-532Do 532-3 #3-6,8

25x2 - 4y2 = 100Put into standard form

What axis do the intercepts lie on?

What are the intercepts?

The transverse axis is the line segement that has the intercepts as its endpoints.What is the length of the transverse axis?


MB4310/22/08Lomas

HW: Read 528-532Do 532-3 #3-6,8

To graph 25x2 - 4y2 = 100

we still don't have enough info, but what do we know so far?

What do we still need to know?


MB4310/22/08Lomas

HW: Read 528-532Do 532-3 #3-6,8

The asymptotes are two lines that will guide us in graphing hyperbolas

y = xba

-ba

y = x

Find the asymptotes of 25x2 - 4y2 = 100and graph


MB4310/22/08Lomas

HW: Read 528-532Do 532-3 #3-6,8

What axis is the tranverse axis a segment of?What is the length of the transverse axis?What are the equations of the asymptotes?Graph.

3x2 - 12y2 = -24


MB4310/22/08Lomas

HW: Read 528-532Do 532-3 #3-6,8

What is the center of this hyperbola?What are the equations of the asymptotes?Graph.

(x-2)2 (y+3)2

9 25- = 1

Technology

Hyperbolas T