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Parabola
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Parabola
A parabola is a plane conic section curve formed by the intersection of a right circular cone and a plane parallel to a side of the cone. Mathematically, a parabola is the two-dimensional graph of a second-degree or quadratic equation or function of the form.
( )
2
2
,
.
y ax bx c
or
f x ax bx c
= + +
= + +
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Conic Sections and Shapes
Hyperbola
Parabola
Circle
Ellipse
Parallel to the side
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Parabolic Curve Applications
In technology
• Parabolic antennas and satellites
• Solar • Parabolic reflection
In physics
• Parabolic trajectory • Zero gravity
Everyday
• Nature’s parabolas • Architecture • Home • Tools
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Trajectory for Launched Object
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Trajectory: NASA Zero G Aircraft
Parabolic Flight 30 thousand feet 28 26 Zero-G 24 22 20 0 20 40
Duration (seconds)
1.8-G 1.8-G
Source: NASA-MSFC
Plane at 45 ° Plane at 45 °
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Parabolic Concentration
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Concentration Examples
Satellite antenna
Source: NASA-GRC
Technology satellite
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Concentration Examples Trough solar dish
Source: Sandia National Laboratories
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Parabolic Dispersion
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Dispersion Examples
Source: www.Pics4Learning.com
Parabolic reflector
Reflected light forms a parallel beam directed straight ahead.
Focus
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Parabolic Curves in Sports
Source: www.Pics4Learning.com
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Parabolic Curves at Home
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Architecture San Francisco Golden Gate Bridge
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Storming Castle Pi: Overarching Problem
The Raving Irrationals are trying to overtake the Castle of Pi. They want to launch burning bales of hay into the castle to drive out the citizens of Pi. When the catapult arm is pulled back to ground level, the hay bale is launched at a distance of 100 feet west of the castle wall. The wall is 35 feet high. The bale clears the wall by a height of 15 feet and lands inside the castle, which is also 100 feet from the wall. The Irrationals come under attack and must retreat from this site. Their new position is 70 feet southwest of the wall. They need to relaunch; however, the wall on this side is 45 feet high. If the castle is 120 feet in diameter, will the hay bales land inside the castle wall or fly over it?
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Application of a Parabola Used with permission by:
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