This answer is a liberal arts version, which deletes some knowledge points and related examples that were originally difficult or not used much, and is suitable for liberal arts students and science students with a slightly poor foundation.

First, set a point or a straight line.

Generally, the coordinates of points or linear equations are needed to do problems. The point can be set to, yes. It should also be noted that the coordinates of many points are independent. For a straight line, if it passes through a fixed point and is not parallel to the Y axis, it can be set as an oblique point, and if it is not parallel to the X axis, it can be set as (m is the cotangent of the inclination angle, that is, the reciprocal of the slope, the same below). If the straight line does not pass through a fixed point, simply set it to y=kx+m or x=my+n when setting the straight line (note: y=kx+m does not represent a straight line parallel to the y axis, and x=my+n does not represent a straight line parallel to the x axis).

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Second, the transformation conditions

Sometimes the conditions given in the topic cannot be used directly or are inconvenient to use directly. At this time, it is necessary to transform these conditions. This is a crucial step for a problem. If the transformation is clever, the amount of calculation can be greatly reduced. The following is a list of conditions that some conversion tools can convert.

Vector: parallel, acute angle or point outside the circle (cross product is greater than 0), right angle or point on the circle, obtuse angle or point inside the circle (cross product is less than 0), parallelogram.

Slope: parallel (slope difference is 0), vertical (slope product is-1), symmetrical (two straight lines are symmetrical about coordinate axis, slope sum is 0, symmetrical about y = x, slope product is 1).

Don't forget to discuss the case that slope does not exist alone when using slope transformation!

Geometry: similar triangles (according to the proportional formula of similar cylinders), isosceles right triangle (congruent structure).

Some questions may be directly brought into conditional solution without transformation, and some questions may be given conditions in many ways. At this time, it is best not to rush to do the problem, but to think about several transformation methods and estimate which method is simpler. Look before you leap.

Third, algebraic operation.

It doesn't count until the conditions are changed. In many topics, a straight line and an ellipse must be connected to use the Vieta theorem of a quadratic equation, but it should be noted that not all topics are like this.

Some problems in analytic geometry may need to calculate chord length, and chord length formula can be used.

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In analytic geometry, area is sometimes needed. If O is the origin of coordinates, the coordinates of two points A and B on an ellipse are sum respectively, and AB and X axis intersect at D, then? (d is the distance from point o to AB; The third formula is not in the textbook. If you want to use the solution, you need to copy the following derivation process).

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Many problems in analytic geometry have moving points or moving straight lines. If the topic involves only one moving point, you can consider setting the point with parameters. If only the moving straight line passing through a fixed point is involved, and the problem involves finding the length and area, it will be easier to set the parametric equation of the straight line.

Some analytic geometry problems may need the range of fractional values, so I also summarize the methods of the range of fractional values of six common types here. Let, where the degree of f(x) is m and the degree of g(x) is n.

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In analytic geometry, there is another method called point difference method. Although the application scope is not large, the problems that can be done by the point difference method will be much simpler than the conventional methods. This kind of problem usually involves the midpoint of the string, so don't forget the existence of difference method when doing the problem. Set the coordinates of two points on the ellipse, subtract the equations of two points on the ellipse, and sort out the relationship between the abscissa and ordinate of the midpoint of these two points and the slope of the connecting line between these two points, or the product of the slope of the connecting line between the two points and the connecting line between the midpoint and the origin. Because the point difference method obtains the slope relationship, it is best to use it together with the conversion slope relationship. (Of course, the premise is that this problem can be transformed by slope. )

In order to give you a better understanding of slip method, I have found some examples of slip method, and I hope you can have a deeper understanding of slip method.

Example 1

Example 2

Example 3

Example 3 is a subject of science, but it is not difficult.

Fourth, the ability requirements

Doing analytic geometry problems first tests people's patience and confidence. In the process of doing the problem, you may encounter a long list of formulas that need to be simplified. At this time, as long as you are in the right direction and insist on calculation, you will definitely see the final result. In addition, the speed and accuracy of operation are also very important. In the real exam, you are absolutely not allowed to do the problem as slowly as usual, so you need to have a certain speed of doing the problem, and you must ensure the accuracy of the operation when doing the problem, because once you make a mistake, it is likely to fall short.

Verb (abbreviation of verb) supplements knowledge

This part mainly talks about some useful formulas, theorems, inferences and so on.

1, about straight lines:

After sorting out the two-point formula of a straight line, we can get this equation:. According to this, you can directly write a straight line through two points. It doesn't matter whether the line connecting these two points is perpendicular to the X axis or the Y axis. For some points with complex coordinates, you can directly substitute this equation and get a straight line passing through two points conveniently.

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2. About the ellipse:

The focus chord chord length of an ellipse is (where α is the inclination angle of a straight line and k is the slope of L). The focus chord midpoint coordinate of the right focus is, and the midpoint coordinate of the left focus chord can be obtained by taking the reciprocal of the abscissa and the ordinate.

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Most of the contents given above are not in the textbook, but this does not mean that these things cannot be used in the examination room. For example, the content of a straight line, when used, first write two-point or oblique. When writing the above form, the marking teacher may not know that you are drawing a conclusion. If you want to use something about an ellipse, you can pretend to calculate it. In fact, if the conclusion is applied, the teacher may not be able to see it. With these conclusions, the amount of calculation can be reduced more or less and the probability of misjudgment can be reduced.

Examples of intransitive verbs

Let's look at some examples. I suggest you do it yourself first, and then look at the problem-solving process. Even if you don't do it, you must watch it. There are many ways involved!

Example 1