直线与圆锥曲线的公共点,是学生比较头痛的问题,经常出错.如何正确地处理这类问题,现举几个例子加以说明.例1求过点(1,-2)且与圆C:(x-2)2+(y-1)2=1相切的直线的方程.错解设所求直线方程为y+2=k(x-1),整理得kx-y-k-2=0.①已知圆的圆心为C(2,1),根据圆心到直线①的距离等于半径,得 The common point between the straight line and the conic is a problem that the students compare the headache and often goes wrong. How to deal with this kind of problem correctly will give a few examples to illustrate. Example 1 The point (1, -2) and the circle C: (x-2) 2+ (y-1) 2 = 1, the equation of the line is tangent to y + 2 = k (x-1) . ① It is known that the center of a circle is C (2,1), and the distance from the center of a circle to a straight line is equal to the radius