The mathematical definition of a parabola is that the distance from the focus to any point on the parabola will be equal to the distance between that point and any point on the directrix. This definition plays a role in the properties of a parabola because the parabola has to be focused around the focus, so if we draw our parabola with the exact distance from the focus to any point to the directrix, we will have the perfect shape that the parabola needs to be. The mathematical definition of a parabola affects its shapes because it determines how fat or skinny it is.2. How does the focus affect the shape of the conic section?
The focus affects the shape of parabolas because the parabola curves around the focus, so that is why the parabola is a curve. It also affects the shape of the parabola because the distances from the focus to the directrix have to be equal in order for the shape of the parabola to be accurate.
3. How do the properties of this conic section apply in real life? One example of a parabola in real life is a bouncing ball. When a ball bounces it travels in a parabolic path. We can say that the ball bounces, goes up to its highest point (or the vertex) and comes back down. Parabolas can also be used in satellite dishes. Satellite dishes work by having waves bounce of from the satellite dish to the center of the satellite which would be the focus.
Parabolas :) This website has more information on parabolas!
Citations:
Parabola image posted from: http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/Gifs/parabola-2.gif
Bouncing ball image posted from:
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0EPWWQKV1Sjm5paUqFrPU0riSln-xwcDPpJQp22xGxLcfteSFGRfV-gvTlXD_OGTpz_WXf8pfA1L-v6ZhftpXNplOhU3A9A91-cvcseMNr0ZGpXVAwnleCzNAPqWs-m2G0gwLrzIVIKg/s1600/Bouncing+Ball.png
Satellite image posted from:
http://dingo.care2.com/pictures/c2c/share/19/190/011/1901182_370.jpg
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