Unit M: Conic Sections

 Parabola

 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?

 This conic section is shaped like an arch, when a right circular cone is cut parallel to the edge of a cone. Any point on the parabola is an equal distance away from the focus or directrix, this allows for the "arch" shape of the parabola.











2. How does the focus (or foci) affect the shape of the conic section?

                  The focus affects the shape of the parabola because "p" determines shape and size. If the focus of the parabola is further away from the vertex, the parabola will be "fatter". Vice versa is true, if the focus is closer to the vertex, the parabola will be "skinnier".










3. How do the properties of this conic section apply in real life?

A real-life application of this conic section is the satellite dish that television companies use to send and receive signals. A satellite is in orbit, sending out signals to Earth, our dishes are facing towards the signals, and the paraboloid shape of the dish creates a perfect angle for the signals to come in, at the focus is the "arm" of the dish, which captures the signal.