IM Geo.6.7 Lesson: Distances and Parabolas

What do you notice? What do you wonder?
[img]data:image/png;base64,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[/img]
[size=150]The applet shows a [b]parabola[/b]. In the applet, move point [math]F[/math] (the [b]focus[/b]) and the line (the [b]directrix[/b]) and observe how the shape of the parabola changes.[/size]
What happens as the focus and directrix move farther apart?[br]
[size=150][size=100]Try to make the parabola open downward (that is, to look like a hill instead of a valley). [/size][/size]What needs to be true for this to happen?[br]
[size=150][size=100]The vertex of the parabola is the lowest point on the curve if it opens upward, or the highest point if it opens downward. [/size][/size]Where is the vertex located in relationship to the focus and the directrix?[br]
[size=150]Move the directrix to lie on the [math]x[/math]-axis and move the focus to be on the point [math]\left(2,2\right)[/math]. Plot a point [math]P[/math], with coordinates [math]\left(6,5\right)[/math]. It should lie on the parabola.[/size][br]What is the distance between point [math]P[/math] and the directrix?[br]
What does this tell you about the distance between [math]P[/math] and [math]F[/math]?[br]
[size=150]The image shows a parabola with focus [math]\left(6,4\right)[/math] and directrix [math]y=0[/math] (the [math]x[/math]-axis).[/size][br][img]data:image/png;base64,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[/img][br]The point [math]\left(11,5\right)[/math] looks like it might be on the parabola. Determine if it really is on the parabola. Explain or show your reasoning.
The point [math]\left(14,10\right)[/math] looks like it might be on the parabola. Determine if it really is on the parabola. Explain or show your reasoning.[br]
In general, how can you determine if a particular point [math]\left(x,y\right)[/math] is on the parabola?[br]
The image shows a parabola with directrix y=0 and focus at F=(2,5). Imagine you moved the focus from F to F'=(2,2). Sketch the new parabola.
How does decreasing the distance between the focus and the directrix change the shape of the parabola?[br]
Suppose the focus were at [math]F''[/math], on the directrix. What would happen?[br]
Close

Information: IM Geo.6.7 Lesson: Distances and Parabolas