Chapter 1 General Theory of Quadratic Curve

Chapter 1 General Theory of Quadratic Curve

Teaching Purpose of this ChapterThrough this chapter, students are familiar with the methods for Simplifying Quadratic Curve Equations on the basis of understanding the Geometric Properties of quadratic curves, so as to understand the classification of quadratic curves.

This chapter focuses on Teaching:(1) various geometric properties of quadratic curves;

(2) simplification methods for quadratic curve equations;

(3) Shape of the quadratic curve.

Teaching difficulties in this chapter:(1) intuitive geometric interpretation of the diameter of the quadratic curve, the diameter of the spline, and the main diameter;

(2) Use the coordinate transformation method and the invariant method to simplify the quadratic curve equation.

Teaching Content of this chapter:

 

§ 0 Preface

 

ITasks in this chapter:

In the Cartesian coordinate system of the plane, the binary quadratic equation

(These are all real numbers ).Quadratic Curve. This chapter will study the quadratic curve equation to obtain some properties of the quadratic curve, then discuss the simplification of the quadratic curve equation, and finally give the classification of the quadratic curve.

IIAgreed mark:

NoteF (x, y)≡ X² + 2xy + y² + 2x + 2y +

Rule =, =, =

So F (x, y) = (x + y +) x + (x + y +) y + x + y +

Record

(X, y) returns x + y +

Then F (x, y) = x (x, y) + y (x, y) + (x, y)

Coefficient Matrix of F (x, y)

A =

It is called the matrix of the quadratic curve F (x, y) = 0. Therefore, the F (x, y) table can be

F (x, y) = (x, y, 1)

Record the records of PHI (x, y) = x² + 2xy + y²

While matrix = is called a matrix of Φ( x, y)

Last, note

= +, = When A * then, = when A else, and

The Algebraic remainder formula of = +

 

Algebra