JPD Home | Ellipses
and Hyperbolas | Contact Me
Exploring
Parabolas (JavaSketchpad)
The activity that is presented here offers an opportunity to
explore the properties of parabolas through a geometric perspective
within your browser window.
There are five areas to explore within this activity:
Top
Directions for Creating and Simulating a
Parabola in the JavaWindow:
- Create a straight line across the bottom of the window named
the directrix.
- Construct a point on this directrix that can be moved
about the line. Try moving it and notice that the line does not
change direction or location but the point will move along this
directrix.
- Construct a point above the directrix anywhere in the window.
This will be our focus. Now we need to construct a
perpendicular bisector of a segment connecting our
focus to the point on the
directrix.
- We can trace this line (click the appropriate button in the
window). Now drag the point on the directrix back and forth
and watch the formation that appears. This appears to be a
parabola. Clear the screen using
the red X in the bottom right of the JavaWindow. Now move
the focus point further or closer from the directrix
(click the red X again to clear the traced lines) and drag the
point on the directrix again or press the show animate
button-button and try the animation.
- We recall the definition of a parabola and we try to
show that this is indeed a construction of a parabola.
Click the button that creates the locus point to represent
all the points of the locus.
Drag or animate the sketch again and notice where that point is.
Click the Show measurements and Construct trace button. Notice
that the distance from the focus to the point of the locus
is equal to the distance from the locus point to the point
on the directrix. (The measurements should be equal
throughout the animation or movement). Check it for a few points.
This is an important part of the definition.
- Hide the traced line by clicking the necessary button and then
hide all the buttons but the animate button. Animate the sketch
and watch the sketch trace out a locus of points and create
a parabola.
- Try to formulate a proof that
this sketch is indeed a parabola.
Top
Constructing A Parabola (Java
Window)
|
|
Top
Tips and Tricks for Working with
JavaSketchpad
- Remember that clicking the red X clears all the
traces
- Try pressing return in the location bar at the top of your
browser to reload the entire window (clear it all)
- Dragging the red points will result in changing the picture
that the window shows you. Experiment with moving lines and
points.
- Try to maximize the size of your browser window to see the
entire picture
- The first time you load this page may take a few moments but
wait and it will work fine.
- Clicking the Animate button once starts the animation.
Clicking it again stops the animation.
If you have an other comments please contact
me
Top
Questions and Explorations
- What does the perpendicular bisector represent when this
activity is compared to the paper folding activity?
- Why is the distance from the directrix to the locus point
measured using a perpendicular line?
- What happens to the parabola when the focus is further away
from the directrix? What about closer to the directrix?
- What do the traced lines represent in relation to the parabola
that is formed?
- What does the point on the directrix represent when it is
moved back and forth?
- How can you construct a proof that this sketch does indeed
represent a parabola? (Hint look at the triangles formed from the
vertices of the focus, locus point, and point on the
directrix)
Top
Definitions and Assistants
- A locus of points is a collection of points or
other objects that satisfies a particular requirement.
- A directrix is a fixed line that serves as a guide
in creating our parabola
- A focus is the point used to determine the
parabola's openness and distance from the directrix.
- A parabola is a collection of points (a locus)
such that the moving locus point is always equidistant from the
focus and the directrix.
- Download GSP File