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GEOMETRY
Contents

CHAPTER 1 QUADRATIC CURVES

1 PARABOLAS - DEFINITIONS AND EQUATIONS
1.1 DEFINITIONS OF PARABOLAS
1.2 STANDARD EQUATIONS OF PARABOLAS WITH VERTEX (0,0)
1.3 GENERAL FORM OF THE EQUATIONS OF A PARABOLA
1.4 LOCUS PROBLEMS

2 ELLIPSES - DEFINITIONS AND EQUATIONS
2.1 DEFINITIONS OF ELLIPSES
2.2 STANDARD FORM OF THE EQUATION OF AN ELLIPSE
2.3 GENERAL EQUATIONS OF AN ELLIPSE
2.4 LOCUS PROBLEMS

3 HYPERBOLAS - DEFINITIONS AND EQUATIONS
3.1 DEFINITIONS OF HYPERBOLAS
3.2 EQUATION OF A HYPERBOLA WITH CENTER AT THE ORIGIN
- HORIZONTAL AXIS
3.3 INFERRING THE SHAPE OF THE HYPERBOLA
3.4 GENERAL EQUATION OF A HYPERBOLA
3.5 LOCUS PROBLEMS

4 TANGENT TO A PLANE CURVE
4.1 POSITIONAL RELATIONSHIPS OF A PARABOLA AND A LINE
4.2 POSITIONAL RELATIONSHIPS OF AN ELLIPSE AND A LINE
4.3 POSITIONAL RELATIONSHIPS OF A HYPERBOLA AND A LINE
4.4 EQUATION OF THE TANGENT LINE TO THE QUADRATIC CURVES (SUMMARY)
CHAPTER 2 VECTORS IN THE PLANE

5 VECTOR OPERATIONS
5.1 DEFINITION OF A VECTOR AND NOTATIONS
5.2 ADDITION, SUBTRACTION, AND SCALAR MULTIPLICATION OF VECTORS

6 COMPONENTS OF A VECTOR AND DOT PRODUCT OF TWO VECTORS
IN THE PLANE
6.1 COMPONENTS OF A VECTOR IN THE PLANE
6.2 DOT PRODUCT OF TWO VECTORS IN THE PLANE
6.3 APPLICATIONS OF THE DOT PRODUCT
6.4 VECTOR EQUATIONS OF LINES AND CIRCLES IN THE PLANE


CHAPTER 3 SPACE FIGURES AND SPACE COORDINATES

7 SPACE FIGURES
7.1 POINTS, LINES, AND PLANES
7.2 THEOREM OF THE THREE PERPENDICULARS
7.3 ORTHOGONAL PROJECTION
7.4 APPLICATION PROBLEMS

8 SPACE COORDINATES
8.1 COORDINATES OF A POINT IN SPACE
8.2 DISTANCE BETWEEN TWO POINTS IN SPACE
8.3 DIVISION OF A LINE SEGMENT IN SPACE
8.4 EQUATION OF A SPHERE