Subject: the focus of a parabola
Name: Lily
Who are you: Student (Secondary)

I have a mathematical assignment which includes applications of parabolas, hyperbolas and ellipses in the real world. I have been searching the internet and now I am ware that most of the applications of parabolas have a connection with what people call "the focus". However, I do not think I clearly understand what "the focus" of a parabola is. Would you please explain it to me? Thank you in advance.


Hi Lily,

One way to define a parabola is to start with a line in the plane, called the directrix, and a point in the plane not on the line, called the focus. The parabola defined by that directrix and focus is every point in the plane that is the same distance from the focus as it is from the directrix.

The applications you are seeing probably rely on the reflective property of the parabola. There is a description of this property and an application in a note called Why are satellite dished parabolic? in the Resource Room at Math Central.

There is a similar reflective property of an ellipse and applications that use this property. For an example go to the section called math beyond school on the first page of Math Central and search for the keyword ellipse.