the last conic section that has significant relation to the world we live in is the hyperbola. The easiest way to imagine this event would be to picture a strong light with a perfectly cylindrical lampshade covering it. The light that infiltrates through the lampshade in the openings creates a hyperbolic curve. A jet plane that flies at a speed of over 770 miles per hour will create a sound wave that will hit the ground and create sound in a hyperbolic shape. The sonic boom will be heard quite some distance from the plane itself as an almost half cone image is given. The interception of the ground, taking place as the plane, forms the curve of the hyperbola. It is not a parabola because it would intercept the cone at the top had there been one. Along the line where the hyperbola hits the ground, all different people in many places hear the same noise just as loud. That is the sonic boom. Another way that the hyperbola is applied to everyday science is in a popular radar system known as LORAN. This system uses foci and hyperbolic curves to determine the location of ships and other such objects.As one can see, there are many formulas that can be derived and applied when using conic sections. Their understanding and comprehension is important for laws pertaining to astronomy, and many other applications as previously mentioned.Mr. Finta, I would just like to let you know that in the original version of this report there was 14 and a half pages with the vertex equations thoroughly covered and with a great proofreading job. The essay was lost on my computer and I had to start from what I last saved it at, 4 pages. I re-built it as best I could but it is nowhere near the quality of its original counterpart as this one was rushed to be completed....
