1, let the tangent equation be y = kx+B. Suppose the slope k of the tangent exists.

2. According to the derivative function, find the tangent slope k. If k does not exist, then the linear equation is directly a function of x= constant, and can be solved by directly substituting the coordinates (x0, y0) of this point.

3. If k exists, substitute the point (x0, y0) into y=kx+b to solve the linear equation.

Expand one's knowledge

Geometrically, a tangent is a straight line that just touches a point on a curve. More precisely, when the tangent passes through a point on the curve (i.e. the tangent point), the direction of the tangent is the same as that of the point on the curve. In plane geometry, a straight line with only one common intersection with a circle is called the tangent of the circle.

Geometric definition

P and Q are two adjacent points on curve C, and P is a fixed point. When point Q is infinitely close to point P along curve C, the limit position PT of secant PQ is called the tangent of curve C at point P, and point P is called the tangent point. A straight line PN passing through the tangent point P and perpendicular to the tangent line PT is called the normal of the curve C at the point P (the idea of infinite approximation).

Note: In plane geometry, a straight line with only one common intersection with a circle is called the tangent of the circle. This definition does not apply to general curves. PT is the tangent of curve C at point P, but it has another intersection with curve C; On the contrary, although the straight line L has only one intersection with the curve C, it is not the tangent of the curve C. ..

Algebraic definition

In advanced mathematics, if a function has a derivative somewhere, then the derivative here is the slope of the tangent line passing through it, and the straight line formed by this point and the slope is the tangent line of the function. The concept of tangent angle: the angle whose vertex is on the circle, one side intersects with the circle and the other side is tangent to the circle is called tangent angle. It is the third angle related to the circle after the central angle and the peripheral angle. This angle must meet three conditions:

The vertex is on the circle, that is, the vertex of the angle is the tangent point of a tangent of the circle; One side of the angle intersects the circle, that is, one side of the angle is the ray where a chord of the tangent point is located; The other side of the angle is tangent to the circle, that is, the other side of the angle is a ray on the tangent line with the tangent point as the endpoint. They are the criteria for judging whether an angle is a tangent angle, and all three are indispensable;

The tangent angle can be regarded as a special case of the circumferential angle, that is, the angle formed when one side of the circumferential angle rotates around the vertex to be tangent to the circle. Therefore, the tangent angle has similar properties to the circumferential angle.

Chord tangent angle theorem: the chord tangent angle is equal to the circumferential angle of the arc pair it clamps, which is one of the important theorems to prove the equality of the internal angles of the circle. Secant theorem: the tangent and secant of a circle are drawn from a point outside the circle, and the length of the tangent is the middle term in the length ratio of the two lines where this point intersects the secant. Inference: The product of two secant lines leading from a point outside the circle to the intersection of each secant line and the circle is equal.