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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.