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Published byCecil Ross Gilmore Modified over 5 years ago

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1 20.1 Taxicab Geometry The student will learn about: other geometric figures in Taxicab Geometry. 1

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Introduction We are going to examine a variety of geometric figures that use distance in their definitions.

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Definitions Let A (0, 0). Graph all the points P so that PA = 6. What is the name given to this set of points? A

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Definitions Just as a circle is all the points equidistant from a fixed point the other conics may be defined with respect to distance. A parabola is all the points equidistant from a fixed point (focus) and a fixed line (directrix).

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Taxicab Parabolas Consider the line that is the x-axis and the point F(0, 2). Find the set of points P so that the taxicab distance from the line is equal to the distance PF.

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Taxicab Parabolas Find all the points equidistant from the point and line given below. 6 6

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Definition Given two points A and B (foci), an ellipse is all the points P so that │ PA + PB │ = d where d is some fixed positive constant. After view the examples given be able to make and observation about d.

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Taxicab Ellipse Consider the two points A(0, 0) and B(6, 0). Find the set of points P so that the │ AP + BP │ = 10 AB

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Taxicab Ellipse Consider the two points A(0, 0) and B(5, 5). Find the set of points P so that the │ AP + BP │ = 14 A B

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Taxicab Ellipse Consider the two points A(0, 0) and B(4, 2). Find the set of points P so that the │ AP + BP │ = 12 A B

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Definition Given two points A and B (foci), a hyperbola is all the points P so that │ PA - PB │ = d where d is some fixed positive constant.

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Taxicab Hyperbolas Consider the two points A(0, 0) and B(6, 6). Find the set of points P so that the │ AP - BP │ = 4

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Taxicab Hyperbolas Consider the two points A(0, 0) and B(6, 2). Find the set of points P so that the │ AP - BP │ = 4

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14 Summary. We learned about taxicab ellipses. We learned about taxicab hyperbolas.

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With the remaining class time lets work on our homework assignment 20.1.

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Assignment: §20.1 and Ideal City

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