1)The mathematical definition of a parabola is that the distance from the focus to the parabola is the exactly same distance from the parabola to the diretrix at a ninety degree angle. With this definition, we can find and locate the coordinates that are exactly on the parabola and if we connect all the dots with a line, we have just drawn the shape of a parabola.The directrix in this definition also determines the direction that the parabola opens to. If the directrix is x=?, then the parabola will open left or right and if y=?, then the parabola will open up or down.
2)This definition also affects the value of p on a parabola and p determines if the parabola will be wide or skinny. The smaller the value of p is, the skinnier the parabola and the bigger the value of p is, then the wider the parabola will look.
3)Dishes show the importance of the focus in a paraboloid object. By speaking into the focus, it splits up the sound waves at the paraboloid shape and then send those waves behind the speaker. The paraboloid shape on the other side cathces these sound waves and redirects all of the sound waves back to its focus. This happens because the shape of a parabola is curved and that curved shape is what allows waves to be split or redirected at the focus.
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