Send the link below via email or IMCopy
Present to your audienceStart remote presentation
- Invited audience members will follow you as you navigate and present
- People invited to a presentation do not need a Prezi account
- This link expires 10 minutes after you close the presentation
- A maximum of 30 users can follow your presentation
- Learn more about this feature in our knowledge base article
Do you really want to delete this prezi?
Neither you, nor the coeditors you shared it with will be able to recover it again.
Make your likes visible on Facebook?
Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.
Transcript of Hyperbola's
Table of Contents
Chapter 1: History and Origin Of Conic
Chapter 2: Diagram (labeled)
Chapter 3: "Real World" Applications
Chapter 4: A Poem of Conic
Chapter 5: How to derive the formula for the Conic
Chapter 1.......page 5
Chapter 2.......page 6
Chapter 3.......page 7
Chapter 4.......page 8
Chapter 5.......page 9
History and Origin Of Your Conic
Fact: The hyperbola derives from the greek meaning " over-thrown" or excessive. It was believed to be coined by Apollonius of Perga.
A hyperbola is an open curve with two branches where intersection of a plane with both halves of a center. The plans does not have to be parallel to the axis of the center; the hyperbola will be symmetrical in any case.
Origin of A Hyperbola:
"Real World" Applications
Example 1: Hyperbolas often used on sundials. The shadow of the tip of a pole traces out a hyperbola on the ground over the course of a single day although the exact shape varies with location and the time of year.
Example 2: Trilateration. This is a process that involves locating a particular point based on the differences in the distances between it and given points - for example, if a phone is near three cellular towers, hyperbola can be used to locate exactly where it is in relation to them
Example 3: A household lamp casts hyperbolic shadows on a wall.
Example 4: Dulles Airport, designed by Eero Saarinen, is in the
shape of a hyperbolic paraboloid. The hyperbolic paraboloid is a three-dimensional curve that is a hyperbola in one cross-section, and a parabola in another cross section.
Example 5: When two stones are thrown simultaneously into
a pool of still water, ripples move outward in concentric circles.
These circles intersect in points which form a curve known as the hyperbola.
Poem For Hyperbola
Like to branches going in the same direction
trying to find different things
One looking for a positive light
Where the other is trying to reach something negative
two things looking for something else
but their called the same thing
their called..their called a hyperbola
their vertical and horizontal axis
most of them equal 1
that has mostly been the sum of
some of them.
How To derive Formula........
When the center is at the origin and the principal is the x axis, the equation of the hyperbola is x2/a2- y2/b2.
The vertices are at (a, 0) and (-a, 0). The length of the transverse axis is 2a. The extremities of the conjugate axis are (0, -b) and (0, b) and its length is 2b. The foci are on the transverse axis at (c,0) and (-c, 0) where c= a2 +b2 .
When the center is at the origin and the principal axis is the y axis, the equation of the hyperbola is y2/a2- x2/b2.
The vertices are at (0, a) and (0, -a). The length of the transverse axis is 2a.. The extremities of the conjugate axis are (-b, 0) and (b, 0) and its length is 2b. The foci are on the major axis at (0, c) and (0, -c) where c= a2 +b2.