1. Understand the actual background of conic curve, and understand the role of conic curve in describing the real world and solving practical problems;

2. Master the definition, geometry, standard equation and simple properties of ellipse and parabola;

3. Understand the definition, geometry and standard equation of hyperbola, and know its simple geometric properties;

4. Understand the simple application of conic curve;

5. Understand the concept of the combination of numbers and shapes

Second, the test site review 1- ellipse:

1. Using the undetermined coefficient method to solve the standard equation;

(1) There are two methods to solve the elliptic standard equation, one is based on the definition directly, and the other is the undetermined coefficient method (first qualitative, then finalize the design, then determine the parameters).

The standard equation of ellipse has two forms. The so-called "standard" means that the center of the ellipse is at the origin and the focus is on the coordinate axis. The position of the focus F 1 and F2 determines the type of the standard equation of the ellipse, which is the positioning condition of the ellipse. Parameters A and B determine the shape and size of the ellipse, which are the forming conditions of the ellipse. For the equation x 2/m+y 2/n =1,m >；; 0, n>0 If m>n, the focus of the ellipse is on the X axis; If the focus of the m< ellipse is on the y axis. When the focus position is not clear, we should pay attention to classified discussion. (2) When the focus position of an ellipse is not clear and its standard equation cannot be determined, the equation can be set as x 2/m+y 2/n = 1, m > 0, n B& gt；, which can avoid discussion and complicated calculation, ax 2+by 2 =1(a > 0, b & 0), this form is more convenient in solving problems.

2. The application of ellipse definition:

The sum of the distances between a fixed point and two fixed points F 1 and F2 on the plane is equal to a constant 2a, and when 2a >: |F 1F2 |, the trajectory of the moving point is an ellipse; When 2a=|F 1F2 |, the trajectory of the moving point is the line segment f1F2; Dang2a

3. Geometric properties of ellipse:

(1) Let any point on the equation of elliptic circle X 2/A2+Y 2/B 2 =1be P, then OP 2 = X 2+Y 2. When x=-a, A has the maximum value, and P is on the long axis A 65433.

(2) Any point p on the ellipse and two focal points F 1F2 form a triangle called a focal triangle with a circumference of 2a+2c.

(3) A focus, the center of the ellipse and the endpoint of the short axis form the side length of a right triangle, and A 2 = B 2+C 2.

4. Intersection point of straight line and ellipse

When solving problems about ellipses, we should draw pictures first, pay attention to the geometric meaning of equations and the auxiliary role of graphics in solving problems, turn the learning of geometric figures into the learning of algebraic expressions, and at the same time understand the geometric meaning of algebraic problems. The thinking method of combining numbers and shapes is the basic thinking method in analytic geometry. The essence of analytic geometry is to use algebra to study geometry, such as solving trajectory equations and range problems, which are almost all related to functions. In essence, geometric conditions (properties) are expressed by verbs.