- 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 conic section - parabola - has the same distance from the focus to the directrix (from any point).That definition plays a role in how a parabola is formed because the double napped cone is intersected by a plane ( which is parallel to the generator line).
- 2. How does the focus (or foci) affect the shape of the conic section?
If "p" is a big number then the parabola sketched on the graph will be wider. So, if "p" is a small number it will be sketched out as a skinny parabola. Remember that the focus is inside the parabola and the distance from the focus to the vertex and the vertex to the directrix is equal to "p".
- 3. How do the properties of this conic section apply in real life? (While using the exact examples I gave you may be acceptable, I will be looking for some research, creativity, and thought. There is a lot out there!)
Car headlights are an example of parabolas in real life. The light is reflected from the focus of the parabola outwards to the other parabola. In reflecting telescopes the primary mirror is parabolic and directs light to the diagonal mirror, reflecting to the focus and parabolic mirror.
Citations: Website: http://www.math.rutgers.edu/courses/251/Lab_Backgrounds/Lab3_Background.html
Parabola images from: http://ts2.mm.bing.net/th?id=H.4989898170565233&pid=15.1 http://people.richland.edu/james/lecture/m116/conics/parabola1.gif , http://hotmath.com/hotmath_help/topics/focus/parabola.gif
Headlight Image from: http://ts2.mm.bing.net/th?id=H.4923686944899993&pid=15.1
Reflecting telescope image from: http://astro-canada.ca/_en/a2304.php
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