1. The positional relationship between straight line and conic curve.
This kind of problem mainly adopts analytical discriminant, including △ > 0, the straight line intersects the conic curve; δ = 0, the straight line is tangent to the conic curve; △& lt； 0, the straight line is separated from the conic curve. If a=0, b≠o, a straight line intersects with a conic curve and has an intersection point. Note: When setting the linear equation, the slope does not exist and can be discussed separately in advance.
2. The combination of conic curve and vector.
This kind of problem mainly uses the equality, parallelism and verticality of vectors to find the quantitative relationship between coordinates, and often combines the relationship between roots and coefficients to reflect the idea of combining numbers and shapes to simplify calculation.
3. Fixed point fixed value.
The fixed point problem can be explored with special values or symmetry first, and then the conclusion can be proved, which can simplify the operation.
Reasoning and calculating directly, and eliminating variables in the process of calculation and reasoning, so as to get a fixed value.
4. The problem of maximum value and parameter range.
There are two common solutions: geometric method and algebraic method.
If the conditions and conclusions of the topic can clearly reflect the geometric characteristics and significance, we should consider using the graphic properties to solve it, which is the geometric method. If the conditions and conclusions of the topic can reflect a clear functional relationship, the objective function can be established first, and then the maximum value of this function can be found. This is the algebraic method.
When solving the problem of maximum and range by algebraic method, we often have to consider the following five aspects:
The inequality relation is constructed by discriminant, so as to determine the range of parameters. Using the range of known parameters, we can find the range of new parameters. The core of solving this kind of problem is to establish the equivalence relation between two parameters. Using the implicit or known inequality relationship to establish inequality, so as to find out the range of parameters.
Using basic inequality to find the range of parameters. The range of parameters is determined by solving the range of functions.
Conic curves and fixed points:
A conic curve is a curve obtained by cutting a plane into a conic surface. Conic curves include ellipse (circle is a special case of ellipse), parabola and hyperbola. The ancient Greek mathematicians who originated more than 2000 years ago first began to study conic curves.
The (incomplete) unified definition of conic: the locus of a point whose ratio of the distance r from a point to a point on a plane to the distance d from a point to a straight line is constant e=r/d is called conic. When e> 1 is hyperbola, when e= 1 is parabola, when 0
The fixed point is called the focus of the conic, the fixed line is called the directrix, and e is called the eccentricity.