**A GEOMETRIC CONSTRUCT
OF A PARABOLA**

**Assignment 6**

**by**

**Gloria L. Jones**

** **

** **

In this assignment the geometric construction of a parabola will be examined whether than from an algebraic perspective. A parabola is the set of all points that are equidistant from a fixed point (the focus) and a line (the directrix).

Given a fixed point **F **for
the focus and segment **AB** for the
directrix, we will construct a perpendicular line through a random point E on
segment AB as shown:

Next, we will form segment **FE **and construct the perpendicular bisector of this segment (line m):

Now we can find the point of intersection of line m and the green line (call it point P). Then connect segment PF and segment PE, the congruent sides of the isosceles triangle formed, thus constructing a point P equidistant from the focus and the directrix:

As point E moves along segment AB, the trace of the equidistant point P is generated. Click here to view animation and trace of point P and resulting parabola. Click here to view trace of the tangent line at point P and resulting parabola.

In the final sketch, GSP is used to generate the locus of points equidistant from a fixed point (focus) and the directrix line: