关于圆的切线方程的推导已知O的方程为（x-a（y-b，r2以及一点P（x,y）,求过点P的O的00切线方程.沙得akm，b11xkm，yo11oy-b0x-a0,从而有过点P的圆的切线方程的斜率为x一ak，o1yb0因为点P在圆上，所以有yyoxa(oxxyboo展开得x2y2axby-ax-by-xx-yy，Ooooooo将上式整理得(x-x)(xy)(y00b)，当点P在O外时，存在两条关于O的切线方程，如图所示00设O的切线方程为y=kxm,由于切线过点P(x,y)得y=kx一kxy,2220022200化为一般式kx一y一kxy=022200由方程(x-a(y-b=r2得点O的坐标为(a,b)因为直线与圆相切，所以点O到切线的距离等于圆的半径r.ak一b一kxy,),)故有2200=rr2x21=ak一b一kxy尢k21222002a2k2k2x2一2ak2x一2abk2aky2bkx一2kxyb2y2一2by一k2r2一r2=02202022020200002k22k22x2一2ax一r2)一2k(ab一ay一bxxy00200-一r2-L2k(ab一ay一bxxy20000)C2y2一2by0000一r2=0一y000(ab一ay一bxxy)r(x一a(yb一00/0a-x0由上述方程y2=k2x一k2x0y0得0000y2y0一b(ab一ay一bx+xy)r(x一a+(yb一0000a一xr2(ab一ay一bxxy)r(x一a+(x000/0a一x0000