题目已知直线l:y=kx+1(k∈R),双曲线c:x~2-y~2=1.试求k的取值范围使直线l与双曲线c:(1)只有一个公共点,(2)有两个公共点,(3)没有公共点.分析直线与二次曲线的公共点个数问题即直线方程与曲线方程构成的方程组的解的个数问题,因此问题转化为确定方程组的解的个数问题. Subject known line l: y = kx + 1 (k ∈ R), hyperbolic c: x ~ 2-y ~ 2 = 1. The range of the trial k so that the linear l and hyperbolic c: (1) only A common point, (2) There are two common points, (3) There is no common point.Analysis of the number of points of the common point of the straight line and the quadratic curve The problem of the number of solutions to the system of equations formed by the linear equation and the curve equation The problem is translated into the problem of determining the number of solutions to the system of equations.