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20.1 Taxicab Geometry

The student will learn about

other geometric figures in Taxicab Geometry.

1

1

Introduction

- We are going to examine a variety of geometric

figures that use distance in their definitions.

Definitions

Let A (0, 0). Graph all the points P so that PA

6.

What is the name given to this set of points?

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 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.

Taxicab Parabolas

Find all the points equidistant from the point

and line given below.

6

6

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 Ellipse

Consider 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 Ellipse

Consider the two points A(0, 0) and B(5, 5). Find

the set of points P so that the

AP BP 14

B

A

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

B

A

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 Hyperbolas

Consider the two points A(0, 0) and B(6, 6). Find

the set of points P so that the

AP - BP 4

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

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 20.1 and Ideal City

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