The second-order conclusion of conic curve is as follows:
A, the quality of the ellipse:
The major axis of a circle is a function of eccentricity e and major axis length a, that is, 2a = 2/( 1-e 2). If the focal length of an ellipse is f, the eccentricity is e, and the length of its major axis is 2a, it is 2=a2-br2, and b = a (1-e 2). The geometric center and gravity center of the ellipse coincide and are located at the center point of the circle.
Second, the nature of hyperbola
1, the major axis of hyperbola is a function of eccentricity and radius of imaginary axis, that is, 2a = 2//e 2-1l.
2. If the focal length of hyperbola is f, eccentricity is e and the length of major axis is 2a, then F2 = A2+B 2, and b=a(en2- 1).
3. The geometric center and gravity center of hyperbola coincide and are located at the center point of hyperbola.
Third, the nature of parabola
1, the focus of parabola is at the free fixed point, and the geometric center and gravity center are on the symmetry axis of parabola.
2. Parabolic eccentricity e= 1 is a special conic curve. The focal length of parabola is f, and the geometric center and gravity center are located on the parabola symmetry axis, which satisfies f=a/44.
Intersection of straight line and conic curve: Let the equation of straight line L be ax+byc=0, and circular curve F(x, y)=0. Then the number of intersections of straight line L and conic F(x, y)=0 is:
1, if l is not greater than the quadratic curve F(x, y)=0, then the intersection number is 0 or 2.
2. If l passes through the center point of the conic F(x, y)=0, the number of intersections is 2.
3. If l passes through the vertex of the conic F(x, y)=0, the number of intersections is 1.
4. If l passes through the focus of conic F(x, y)=0, the number of intersections is 1 or 2.
In short:
The second-order conclusion of conic curve is an important content in high school mathematics, which plays an important role in mastering the basic concepts and solving methods of conic curve. When learning and mastering these conclusions, we need to understand them carefully, do more exercises and strengthen our understanding and application ability of mathematical concepts.