PARABOLAS

By:

DEBORAH ECKSTEIN

For assignment six I have chosen to do the construction of a parabola. A parabola is the set of points equidistant from a line, called the director, and a fixed point, called the focus. We will assume the focus is not on the line and construct a parabola given a fixed point for the focus and a line (segment) for the director.

There are many different ways to construct a parabola in GSP and this assignment ask us to show three of them:

a. Use an Action Button to generate the parabola from an animation and trace of a constructed point.

b. Repeat 9a with a trace of the tangent line at the constructed point.

c. Use the locus command to generated the parabola from a constructed point or the tangent line at that point.

A.Let's construct our first parabola using an action button from an animation and trace of a constructed point.

1)Construct a line AB, which is called the directrix, and put any point on that line that we will call point C. Then put a point D somewhere not in the line, which we call the focus.

2)Now construct a perpendicular bisector through our point C and also create a line segment connecting D to C and construct its midpoint

3)Now we will construct a perpendicular bisector through our midpoint and label the intersection of the two perpendicular bisector at j

4)To get the animation of our parabola you would select point j to trace and point C to be the animation point.

Click here to see the animation of the parabola we just created!

B. Now let's construct a parabola with a trace of the tangent line at the constructed point.

1)We repeat steps 1-3 from part A

2) let the trace point be the perpendicular bisector j and leave C as our animation point.

Click below to see the new construction of our parabola!

C. Now as a third way to construct a parabola we will use the locus command to generated the parabola from a constructed point or the tangent line at that point.

1)Here you will once again repeat the steps you did in part A

2) Select C and j on the construction and go to the construction button in the menu and select locus. A parabola will then be drawn.

Now we have three different ways to construct the parabola based off of one construction!!!!