1. What is the mathematical definition of this conic section and how does that definition play a role in the properties of the conic section and how it is shaped or formed?
The mathematical definition of the conic section (parabola): the distance from the focus from any point on the parabola is perpendicular to the directrix. It has an equal distance between the focus and the vertex and an equal distance between the vertex and the directrix.
2. How does the focus (or foci) affect the shape of the conic section?
P is the distance from the vertex to the focus. It affects the shape of the conic section depending on how large the # 'p' is. For example, the more smaller the # 'p' is -> the more narrow the parabola will be. The more larger the # 'p' is -> the more wider the parabola will be!
3. How do the properties of this conic section apply in real life?
One example of how this conic section is applied in real life would be the 'whisper dish.' The whisper dish is a large plate that is able to reflect the sound waves and signals towards the other whisper dish. By talking into the focus of one dish, it may bounce off and go towards the focal point of the other whisper dish. The symmetrical shape and distance allows the whisper dish to signal and bounce off to each other.
Citations:
Parabola image from: http://people.richland.edu/james/lecture/m116/conics/parabola.gif
Parabola (p) image from: http://upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Parabola_with_focus_and_arbitrary_line.svg/400px-Parabola_with_focus_and_arbitrary_line.svg.png
Whisper dishes video from: http://www.youtube.com/watch?v=y26wYeOg_gU
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