Knowledge points about "circle" in mathematics of senior high school entrance examination

# Senior High School Entrance Examination # Getting started is not a long journey; If you don't accumulate small streams, you can't become rivers and seas. For the exam, it will be easier to pass the exam if you make a little progress every day and have a solid foundation. I will provide you with the knowledge points about "circle" in the mathematics of the senior high school entrance examination, consolidate what you have learned at ordinary times and use it flexibly, so that you will be more handy in the exam. Come and have a look!

The positional relationship between circle and straight line

Link: the positional relationship between a circle and a straight line (i. 5）

On the plane, the general method to judge the positional relationship between the straight line Ax+By+C=O and the circle X 2+Y 2+DX+EY+F = 0 is

Discuss the following two situations:

(1)y =(-C-Ax)/b can be obtained from Ax+By+C=O, where b is not equal to 0,

Substituting x 2+y 2+dx+ey+f = 0, the quadratic equation f(x)= 0 is obtained.

Using the symbol of discriminant B 2-4ac, the positional relationship between a circle and a straight line can be determined as follows:

If B2-4ac "0, the circle and the straight line have two intersections, that is, the circle and the straight line intersect.

If b 2-4ac = 0, the circle and the straight line have 1 intersections, that is, the circle is tangent to the straight line.

If b 2-4ac

(2) If B=0, the straight line is Ax+C=0, that is, x =-c/a. It is parallel to the Y axis (or perpendicular to the X axis).

Change X 2+Y 2+DX+EY+F = 0 to (X-A)2+(Y-B)2 = R2.

Let y=b and find two x values x2 of x 1. We specify x 1.

When x=-C/Ax2, the straight line is separated from the circle.

When x 1

When x=-C/A=x 1 or x=-C/A=x2, the straight line is tangent to the circle.

Calculation formula of circle

1. The circumference of the circle C=2πr=πd2. The area of the circle S=s=πr? 3. Sector arc length l=nπr/ 180

4. Sector area S=nπr? /360=rl/25。 The lateral area of the cone is S=πrl.

Equation of circle

Standard equation of 1. circle

In the plane rectangular coordinate system, the standard equation of a circle with point O(a, b) as the center and R as the radius is

（x-a)^2+(y-b)^2=r^2

2. General equation of circle

After expanding the standard equation of a circle, moving terms and merging similar terms, the general equation of a circle can be obtained as follows.

x^2+y^2+Dx+Ey+F=0

In fact, compared with the standard equation, D =-2A, E =-2B and F = A 2+B 2.

Related knowledge: Eccentricity of circle e=0. The radius of curvature of any point on the circle is R.

The definition of circle and the related quantity of circle

1. A graph composed of all points whose distance from a plane to a fixed point is equal to a fixed length is called a circle. The fixed point is called the center of the circle and the fixed length is called the radius.

2. The part between any two points on the circle is called arc, or arc for short. An arc larger than a semicircle is called an upper arc, and an arc smaller than a semicircle is called a lower arc. A line segment connecting any two points on a circle is called a chord. The chord passing through the center of the circle is called the diameter.

3. The angle of the vertex on the center of the circle is called the central angle. The angle at which the vertex is on the circumference and both sides intersect with the circle is called the circumferential angle.

The circle passing through the three vertices of a triangle is called the circumscribed circle of the triangle, and its center is called the outer center of the triangle. A circle tangent to all three sides of a triangle is called the inscribed circle of the triangle, and its center is called the heart.

5. There are three positional relationships between a straight line and a circle: there is no separated common point; There are two common * * * points intersecting; A circle and a straight line are tangent at a common point. This straight line is called the tangent of the circle, and this common point is called the tangent point.

6. There are five positional relationships between two circles: if there is nothing in common, one circle is called external separation outside the other circle, which is called internal separation; If there is a common point, a circle is called circumscribed by another circle; There are two things in common called intersection. The distance between the centers of two circles is called the center distance.

7. On a circle, a figure surrounded by two radii and an arc is called a sector. The developed diagram of the cone side is a fan. The radius of this sector becomes the generatrix of the cone.