**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