Core knowledge points are the foundation. Many students can't remember the eccentricity formula and range of conic problems, especially small problems, such as ellipses and hyperbolas. Asymptote equation, who focuses on the hyperbola on the X axis and the Y axis respectively, is also stupid and confused, and will naturally make mistakes when doing problems.

2, computing power and speed

It is relatively easy for students with strong computing ability to learn conic curves, and doing more problems can improve their computing ability. In the future, you can try to train yourself to get simultaneous quadratic equations by oral calculation, and then get the discriminant, the sum of two roots and the algebraic expression of the product of two roots.

Of course, we should also master some tips to solve problems and speed up operation.

3, thinking routines

Many students say that we can't start with the problem of conic curve, which is very difficult from the surface. Teacher's suggestion: Doubt can't be recovered, even if you do nothing. Most of the major problems of conic curves have the same trilogy: one set, two sets, and three-dimensional Yatta theorem.

Suppose that the coordinates of two intersections of a straight line and a conic curve are (x 1, y 1) and (x2, y2) respectively, and the equation of the straight line is y = kx+b.

Simultaneous: Get simultaneous quadratic equation through quick calculation or oral calculation.

Vieta Theorem 3: Discriminant, the sum of two roots and the product of two roots are obtained immediately after the quadratic equation is obtained.

After the trilogy, look at the conditions and requirements given by the topic. For example, when it comes to chord length, "the relationship between root and coefficient" is often used instead of calculating chord length (that is, applying chord length formula); When it comes to the midpoint of a chord, the "point difference method" is often used to set it instead of looking for it. The slope of the straight line where the chord is located and the coordinates of the chord midpoint are linked and transformed with each other. To sum up, the equal relationship of evaluation columns and the unequal relationship of range columns are usually solved by combining discriminant with basic inequality.

4. Conic curve solving methods and skills are summarized.