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20.1 Taxicab Geometry

The student will learn about:

other geometric figures in Taxicab Geometry.

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Introduction

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

DefinitionsLet A (0, 0). Graph all the points P so that PA = 6.

What is the name given to this set of points?

A

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).

Taxicab ParabolasConsider 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.

Taxicab ParabolasFind all the points equidistant from the point and line given below.

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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.

Taxicab EllipseConsider the two points A(0, 0) and B(6, 0). Find the set of points P so that the

│AP + BP│= 10

A B

Taxicab EllipseConsider the two points A(0, 0) and B(5, 5). Find the set of points P so that the

│AP + BP│= 14

A

B

Taxicab EllipseConsider the two points A(0, 0) and B(4, 2). Find the set of points P so that the

│AP + BP│= 12

AB

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.

Taxicab HyperbolasConsider the two points A(0, 0) and B(6, 6). Find the set of points P so that the

│AP - BP│ = 4

Taxicab HyperbolasConsider 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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Summary.

• We learned about taxicab ellipses.

• We learned about taxicab hyperbolas.

With the remaining class time lets work on our homework assignment

20.1.

Assignment: §20.1and Ideal City