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# Real Life Applications of Conic Sections

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## Jamie Chem

on 5 May 2014

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#### Transcript of Real Life Applications of Conic Sections

Real Life Applications of Conic Sections
design by Dóri Sirály for Prezi
Definition: A circle is a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Definition: A parabola is the set of all points in a plane that are equidistant from a fixed point, the directrix, and a fixed point, the focus, that is not on the line.
Circles
The End
Parabolas
Definition: An ellipse is a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane that does not intersect the base.
Ellipses
Definition: A symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
Hyperbolas
By: Jamileh Chemaissem & Micah Maglasang
Example: Light Pink Sunflower
Average Diameter: 4 in.
Center: (0,0)
Equation of Circle: x^2+y^2=4
r = 2 in.
seeds
The circle is the most suitable shape for the seeds of the sunflower because it maximizes the number of seeds that can be packed into a seed head
Example: Bridges
Sydney Harbor bridge

Example: The Oval Office
Measurements
Measurements
Measurements
Length of Major Axis (y-axis): 10.9 m
Length of Minor Axis (x-axis): 8.8 m

Center: (0,0)
a^2 = 10.9 m
a= 3.30 m
b^2= 8.8 m
b=2.97 m
c^2= 10.9 m - 8.8 m
c= 1.45 m
Vertices: (3.30,0), (-3.30,0)
foci: (1.45,0), (-1.45,0)
Equation: (x^2/8.8) + (y^2/10.9) = 1
The Oval Office is in the shape of an ellipse so that the president hears everything. Since the president's desk is situated on one of the focus points, he can hear everything from the other focus point.
Example: Hourglass
Measurements
Length: 9.5 inches
Width: 6 inches

Center: (0,0)
Length of Transverse Axis (y-axis): 9.5 in
Length of Conjugate Axis (x-axis): 6 in
a^2= 9.5 in
a=3.08 in
b^2=6 in
b=2.45 in
c^2=9.5 in + 6 in
c= 3.93 in
Vertices: (3.08,0), (-3.08,0)
Foci: (3.93,0), (-3.93,0)
Asymptotes: y= (3.08/2.45)x
y= (-3.08/2.45)x

Equation: (y^2/9.5) - (x^2/6) = 1
http://www.amazon.com/Hourglass-Sand-Timer-Minute-Cherry/dp/B004N6N4VE
An hourglass is in the shape of a hyperbola because it is the most efficient constricting shape that allows an hourglass to tell how much time has passed.
Height: 118 meters above sea level (lower arc)
Width: 503 meters
Bridges have arches because the semicircular structures distributes compression through its entire form and reduces the effects of tension on the underside of the arch
Equation
(x-251.5)^2= -472(y-118)
Opens:
Down
Vertex:
(251.5, 118)
Focus: (4p=-472/4) =
P=-118 (251.5,0)
Directrix:
y= 236
503m
-118m
y=236
10.9 m
8.8 m
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