1. How do we define a parabola (the locus definition)?
Definition: A parabola is the set of points equidistant from a given point and a given line. The given point is called the focus and the given line is called the directrix.
2. Distribute a copy of the "parabola paper" to each student. Have each student trace out a parabola while I do one at the overhead. The purpose of this is to have students understand the definition of the parabola by locating points which are the same distant to a point as they are to a line.
Parabola Paper
3. Develop the equation for a parabola which opens up and has its vertex at the origin.
Let p = distance from the vertex to the focus.
Then the coordinates of the focus
are (o, p).
The vertex would be (0, 0).
The equation of the directrix would
be y = -p.
4. The four general formulas for parabolas:
5. Examples
