IM Geo.6.7 Lesson: Distances and Parabolas

What do you notice? What do you wonder?
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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]

IM Geo.6.7 Practice: Distances and Parabolas

[size=150]The point [math]\left(6,y\right)[/math] is the same distance from [math]\left(4,1\right)[/math] as it is from the [math]x[/math]-[/size][size=150]axis. What is the value of [math]y[/math]?[/size]
[size=150]A parabola is defined as the set of points the same distance from [math]\left(6,2\right)[/math] and the line [math]y=4[/math]. Select [b]all [/b]points that are on this parabola.[/size]
Compare and contrast the parabolas with these definitions.
[list][*]parabola A: points that are the same distance from [math]\left(0,4\right)[/math] and the [math]x[/math]-axis[/*][*]parabola B: points that are the same distance from [math]\left(0,-6\right)[/math] and the [math]x[/math]-axis[/*][/list]
[size=150]Find the center and radius of the circle represented by the equation [math]x^2+y^2-8y+5=0[/math].[/size]
Match each expression with the value needed in the box in order for the expression to be a perfect square trinomial.
[math]x^2+14x+\boxed{ }[/math]
[math]x^2-\dfrac{1}{2}x+\boxed{ }[/math]
[math]c^2-10c+\boxed{ }[/math]
[math]z^2+z+\boxed{ }[/math]
Write each expression as the square of a binomial.
[math]x^2-12x+36[/math]
[math]y^2+8y+16[/math]
[math]w^2-16w+64[/math]
[size=150]Write an equation of a circle that is centered at [math]\left(1,-4\right)[/math] with a radius of 10.[/size]
[size=150]The density of water is 1 gram per cm³. An object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. Will a solid bar of soap shaped like a rectangular prism with mass 1.048 kilograms and dimensions 5.6 centimeters, 13 centimeters, and 16 centimeters float or sink? Explain your reasoning.[/size]
[size=150]Jada has this idea for bisecting angle [math]ABC[/math]. First she draws a circle with center [math]B[/math] through [math]A[/math]. Then she constructs the perpendicular bisector of [math]AD[/math].[/size][br][img]data:image/png;base64,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[/img][br]Does Jada's construction work? Explain your reasoning. You may assume that the perpendicular bisector of line segment [math]AD[/math] is the set of points equidistant from [math]A[/math] and [math]D[/math].

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