The square position relationship between straight line and circle in high school mathematics.

1. In the plane, the general method to judge the positional relationship between straight line Ax+By+C=0 and circle x2+y2+Dx+Ey+F=0 is to use the symbol of discriminant b2-4ac to determine the positional relationship between circle and straight line 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 b2-4ac=0, the circle and the straight line have 1 intersections, that is, the circle is tangent to the straight line.

If B2-4ac

The square position relationship between straight line and circle in high school mathematics II

Tangent equation of a point on a circle

The tangent equation of any point (X0, Y0) on (x-a)2+(y-b)2 = R2;

(X-a)(X0-a)+(Y-b)(Y0-b)=r*2

If you are in a plane rectangular coordinate system, you can also directly

Linear equation: equation with circle: simultaneous.

If discriminant >; 0, the equation has two roots, that is, a straight line and a circle have two intersections and intersect;

If the discriminant =0, the equation has roots, that is, the straight line and the circle have intersections and tangency;

If discriminant

Judging the square position relationship between straight line and circle in senior high school mathematics

1. If the linear equation y=kx+m, and the equation of a circle is (x-a)2+(y-b)2=r2, substitute the linear equation into the equation of a circle, and eliminate y to get a quadratic equation Px2+Qx+R=0(P≠0) about x, then:

When △ < 0, the straight line and the circle have no common point;

When △=0, the straight line is tangent to the circle;

When △ > 0, a straight line intersects a circle.

2. Find the distance d from the center of the circle to the straight line, and the radius is r..

D>r, the line is separated from the circle, and vice versa.

D=r, then the straight line is tangent to the circle.