# 20.1 Taxicab Geometry - PowerPoint PPT Presentation

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

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20.1 Taxicab Geometry

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### 20.1 Taxicab Geometry

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

A

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