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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:


Directions for Creating and Simulating a Parabola in the JavaWindow:

  1. Create a straight line across the bottom of the window named the directrix.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Try to formulate a proof that this sketch is indeed a parabola.


Constructing A Parabola (Java Window)

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Tips and Tricks for Working with JavaSketchpad

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Questions and Explorations


Definitions and Assistants