The coordinates of a point on a curve can be obtained by first finding a monotone function (for example, y=b? √( 1-x？ /a？ ) and the derivative value of this point is the slope of the tangent passing through this point, so that the tangent equation can be obtained by the point oblique method.
In the rectangular coordinate system, the coordinates of the intersection of a line and a circle should satisfy the equations of the line and the circle, which should be the line Ax+By+C=0 and the circle X? +y？ +Dx+Ey+F=0(D？ +E？ -4F=0), so the relationship between a circle and a straight line can be expressed by the equation Ax+By+C=0, X? +y？ +Dx+Ey+F=0。
If the equations have two equal real number solutions, a straight line is tangent to the circle at the same point, that is, a straight line is tangent to the circle.
Extended data:
The positional relationship between a straight line and a circle can also be judged by comparing the distance d from the center of the circle to the straight line with the radius r of the circle, where when d=r, the straight line is tangent to the circle.
If a straight line intersects a curve at two points, and the two points are infinitely close and tend to overlap, then the straight line is the tangent of the curve at that point. In junior high school mathematics, if a straight line is perpendicular to the radius of a circle and passes through the outer end of the radius of the circle, it is said that the straight line is tangent to the circle.
Here, when "Other Geometry" is a circle or a straight line, there is only one intersection point (common point) between them, and when "Other Geometry" is a polygon, there is only one intersection point between the circle and each side of the polygon. This intersection is the tangent point.
Baidu encyclopedia-tangent and circle