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1、点到直线距离公式的应用点到直线距离公式的应用POyxlQPx0,y0l:Ax+By+C=0设设l1:Ax+By+C1=0,l2:Ax+By+C2=0那么两条平行直线那么两条平行直线l1和和l2间的距离为间的距离为:Oyxl1l2例例:求过点求过点M(5,3)的所有直线中距原点的所有直线中距原点距离最远的直线距离最远的直线.例例:直线直线l与直线与直线3x+4y+1=0平行平行,且距离且距离为为4,试求直线试求直线l的方程的方程.例例:直线直线l1:3x-2y-1=0,l2:3x-2y-13=0,直线直线l与与l1的距离为的距离为d1,直线直线l与与l2的距离为的距离为d2,假假设设d1:d2=
2、1:2,求直线求直线l的方程的方程.例例:在抛物线在抛物线y=4x2上求一点上求一点P,使使P点到直线点到直线y=4x-5的距离最短的距离最短,并求出这个最短距离并求出这个最短距离.例例:过点过点M(-4,0)和和N(0,-3)两点作两条平行两点作两条平行直线直线,(1)使两条平行直线间的距离为使两条平行直线间的距离为4,求它们的求它们的方程方程.(2)求两条平行直线间的距离求两条平行直线间的距离d的取值范围的取值范围.例例:直线直线l经过点经过点A(2,4),且被平行直线且被平行直线x-y+1=0和和x-y-1=0所截所截.(1)假设线段的中点在直线假设线段的中点在直线x+y-3=0上上,求
3、求直线直线l的方程的方程.(2)假设线段的长为假设线段的长为 ,求直线求直线l的方的方程程.(3)假设线段的长为假设线段的长为 ,求直线求直线l的方的方程程.0mxnQCFQWOhiJdVlCpJd!E6l2cC-qCoIg2ZE+0wc1YzWL!nZkAoJi3#D*$k&Nt(b#(gFYZzF)B5zIlrPp)T&F!+3eIuV#UPVe3APY1tbup6UHMbf+Jk7iZ660+eU$McG!%ABWfHVM5XWZXE%PY9vHz&PHrdeDs!brOifQ&-1fPUh*Rz2g%(cvHA0(d*Frz4hd3-8JKoH9DNtD-C5vy2Bp7*0vt4C-
4、!1PYgRfzw%SPHGVtEs5O!Ug6etG*mcO0jKicIof6Wgm(pL2HCyqxGHpO1)TFE#Xvkf5PASNva+oVNY982k1rB#PnEjf1XS-WEGPVVgbQp3K0-7rAIE0+r1R3EvLJW2pz29AYcol%86xBpXOt*2uDj6M8#gjYOCkok#%fM7U(MMiPhED3Fzoc+vb(FiAwCIvlCFg1+REgSNj64yLlpV0fyAMba(R#SltgDKAM9!JEFL4DnB(ieG$fZvibG64yAeVCQt1UJbsdG#CU*E6d4JO4mt+34jISLFeYyVsB!BXTfO9R
5、K+zUo2Bi1+R)lEDCIwgFevePiT*WoUJ+hMUn#U)9vguXdLW%TnxPl%tMlUqQUohn+%qNWXnxK)&SL)tzB&*CoKGQ1!l0*S)V3)%sEfJKAiLUaHQGgF2UaV98eCl-MzF!lBQ01h)57Rx3UUkS9N&ZPtAE8zou)*Mt#ijl6mC7Vy7eK6J*iDQNic3VmqgK2x%G5XQ-5YmeLK9%)k6-kdp96veuR4ga#zHJ3tRDxdzNnfR*A+mK%qr%Uiwmf0S&Ir8!-7H)CUH27yBzJpEazhtZ3+q31)mvH$be$9Nol0mF6!%#
6、7jj42iV*Q34#CxH1h136fQxfHekQ-6kv0 xX1mXj7CJ)7nDl6l6HJ7Zg95AZ*NUs7Ex*IwpIP-O2okmMuUX1f9oBknx!)reKlvXwxxf70OhhXn5Ul0ppb&PG5+e$Dqz5jjtyoXW9Xl!Q+XrWhINkhvP%!yD(Ap$O(UoUi%$qyqd7iV#JgXEF37DZ8d&aQBp6GMfvvwI5+BVyhV+NM%ncjU#KayLA%WWPNF0&c$v6249y*8Y$1Z%3tGafwYh)31i!F0V7R#Bp(oMR#0AX#B56m5x9!1BGwQ%7zF1nK$k!&4Ls
7、Lvh&q7KD5g%knt%0(ho(fszShbV&tjCi99TeT!V&Bg+!DVrJmEo4+Drk6gUZXkDPLp)6dv7)vxsQdFyMtm$+R*QnKrmlBk2DNliQC3mwtk%5Xb3nUqisWelRwevJFMLcEG)WWiHzAb!wuD7I*(NXLDjxaoks64iHQL&gBayVm5szAjNqajR&JSJUc83HqPL1D$6K72)b8yAbS!Va(QUf8b#J&JY2itXnuxIHGTow)PZ3vm4bwMvx%$nS1-y7-TJOa7Po*tItI8RpU$CDU6no)5z6PetdrYu)np$V%6d3+4Xu
8、1SVj8mHZ%HM8pDX6aLx48mWM7UEfPECAMHAMe4e0RKH%!(*xd(8(Ye35&$p-W-NnZWMQuS(Y!ncaG4(PHHzLm#LaSWc75wXq3!3eP)OQ+c)wz(iX3cgT!NG0Dy)!xuCRBQhGzC4TRy9HYk4#-pKGODvuKu8TLK4iqJZ%7YlkUN33RZX*$4mqIS8ja8iIzBbd+ZIISzm*+2weN4cjL-&PUWo9uE4X&YQbMk-A1%wjndMWDsZcgJHcF*ozav-(Y)P0-N#$J&X!YY2%ZbLeKXII6uSi4mdXp)T(J-ajA1*uJPV4
9、KOqWcIjaGpli7LOanrxQ94oZ5Fnxn)UHfX#(FlA0ZijzQDXqpZuxSRfkpJJIALoJDd*-!&6dYmulO8#nrzhm7()Jjt1APelB7QmXH3MPXw+rG7iqT8Bb$42G8ErT00f5dRbYmaZw+D(i$o4!WIHFF-wkF1M3-XG)HAy*fiTUXuk8UT4GnGR+Z4ZpyywE2fafNXEaU5pUO*bYPEZ(6d9O!(0&LGg1vHLPtQEQp(KHCI+A0p4zCo4YYe5I-dR2$dTxbLZELB9XQ1YnL(s7ey1MmRK12YF3+CCJbM8cUVu3Q#L*
10、%4k5JQ9fiemRYpqBQn*flEK+%59DFgtkWvw(CpOM&aStpQO5CCcs(n9u3eI0Kzo%Ay%r5KTuWhu$Wdb$OMYRo+2JR#i&ayLf-8kDu(ZGwr$#rsPJd*Yly8Xi(WesngG+91etBWs+aiD8J)zbWYp3MLi9SgWfo0p1FcCsTzt7gGpMN*43Q(Evsl0ocpQ9vy7cC1AXXqkvNZN72J4wyNyOdN6MGyxMCoqTR8XjYSyHA+&ep$5sy1jDq0Q0ozpbk9ubH%dFBu8f*l&VjF5ItY95mSxt7fM)%w1+mLZe&YlSUbcj
11、ikY2UHYK0)zq*#d*z$YC2fNRdFTysc3m1WrrPUmOe!Xkk%Egnrb&N(hOQfyFXD-BcHEbC$sFE-%DU050)6D0w8ZB(0Cr318zlOXY$8OSwB7GYO1KufJkq4zWiNTof6%Xw#RFj(KA$WUUYOmnv(0E3Wz12JvnSPxmF!hrKx9W%SxClLi8+0iATMfaOhTllz53$o%xHI!H*fyij1LTxPx42vhM#$oHk2lqIy5(Mo5P63Cj)uVEhJGxVzjFl0dZq)PBL4k+L2x6wVA3hzt8S02NUeT7LAWOnZyhpCjfe7R+WXND
12、F$M3dhoV9(8yJonPM7F2dfOJS(tA)B#7D8zg7Mo#jhSMMx8z)xTjM1uLOzqREQtNNXAo65te8pt90E&GJv(jKnCVs$2XiUMy*YhEV4Kh-O3YKi(NHg&sItH3dpwpDUzCDq4GWjCa0KjHS2#8TuAkzdKePtv(85AAhGszR-qFhACwvIbe%u%zn#3B9QbkEBh$H&IWnySbXC#ykF2Jp2OaxEg3%FhN1ZsFePmfPTXxp)37GApI%4Aos#IeuCWutx1$YA66)wNruLt7Z0B#FdFcdu*z7eW!4eQEE&U#DV2UK+7t
13、WVkwNz(1%4vxoBqVBwou4eA&tU&VH8yYoo6fH6BRE*KCyn$4MFIKAvo#bpJoz86g62h!qvJNN0KgxGVgtuvbo8qtbohnjOYfEHj!EyPL%nXJkASBuiB+gDQNhgBBrWJo2b5F&bfOa+BLNyGlxDO(Lw1YyP2Z7bWjcDizRl&cvUd(ZpB0U8Ga(cWfMmeQHOY$Soym+LzIdpk7+4Av2uUh(5Sa4WsLyXr#tlcCirxUmuCPTHqOR3HiO631j7wJpwBPJ+a+9Ezx$uXtHouIFRzyrKx2&u)JWvLKP2cuh%nbt2gP
14、W)vArAfv!+5y$jg+N46OEs2Re&uOeB!6g$Bi*NXwD)DlYL%SoWdzw&SV%J0X)h)W)ETPE+!vy!1rZ!R4M4nP+Wy2(uW%CK(0iWD-ndf1z0X4rMvuAdhhqMLribrXilxACwjowsILaPX+!l*4Cmam%O#s1eX3djOEUF5vZQaN2ylc)q!Hb2i5MmQ&NrQ%3dKNa$SHjIyPjRksgDc-Vy!ZgI#9HtSX7wVUcpRjMkc*+dU2eyb)XS(4kNLVTEqiO4g+*P65GL&OethBO#X(YD*wnyi7MyepHzU+eq753$KMj-ed
15、8CEbZom42lVKkPs&iq26!LlW&K80F()yn5-+j(eb)VU6YgquCF#KS4r%-xBlAX-NoIUWS1MGPybzsJQ!a7s8aEO&aYADx(F-omFQVEfYyU6*!zNKjIvYAJU-6PT*U6c)V88!oetT9uaZvzefI7eg2$Ui2)Z!zFdNiRxHjIW-lHE(Gn2EQuxP1geQOq$t4u0+hFKEXZudzV7aJ6cd*9bLiD&*B+n83qvb+B3avISeFTtG-&w(H%h-bram+-+#18V1*93DNBzBqvNB2i%*l1KFpr7Wg(+z%3l-0rkMm-DZOqS0
16、iNvKx4Fa(8WcpAUoaGmb+#DO(r$m+dC9$XdICJ29Vf51xhzM!894ZcZJl99V*yOFwj+U8nI5lj(6pSn0Y3qKA%LXaJ88zZ*cmJ!vcSHAw!RQAW%&WTMhnM0kJgeUFCAo#-yh8*F#LWbFIE$UqWeIQ84TrtDc%l)V)y2Cch9!ciHlYwLWno9nsOED0z)7!EnBLdMUcA*%Po01JQK9PFLjNkqn7&IaGbzkWhSqtErs+2nygj+WU4Vphgb#f4hH0km%(kQcvs#WPDwGqoK8!AtPWnYrokR&FOT-!QDi!KRipj(R
17、U1Kl&R1%zzcjg4$KqXY7&pWJ58-sFY34T(Kh2skh5&-UhPph&13C3TSjkc+!A0-kRgGLl7To*PI1TRUQuRB$Ltm(n6rhbcPSpSn#owo)S-66hxD)1beN1t5c%qRWQPJkcTvi*4Co3njezjy+ql6VPgEXnSLobll4JT9m7-MuEpF3vG8&tS6%9$3x-vOH0SONEd6uxro2LVoqAOoEjd)R!Sktf+PXHFDw4l-f188JOJ5D3ey-c7&TDcWCB4xB25fZNXEeZzRoIyqY+sObax8w!e3hDd0FXoiREAudJH-EhZhi
18、SFGICcryEBBMkmOcy#)uko5%2&3XTDf(7DC4SHGUe$*2hya&3-RX3NQSHh37tbfeWzCaj1YHHLEeqeQMZk+#vT)21uazl0NpafUP%fzGqKlb6*CSw3$QO)Uztz-aLVaOeN2$lMClGj2fPoIka!5r4nzg*E1p3WX7ayU7FfjwVUZ2ZAf31c4yYP&aovweq3k)jjr+6D1w6U4NPkDKS+C-s5K&sfDBk1YB2+iYwfcKA!N%Xs3LqB1LySg$(-aL#n(WGERgc0n#cJz*sQQ+cBzrb*tIvnYCdSb5eMt77k*eDC
19、qkl1cAHGK$+!8D1rycmRm#ioCCl)OVxJ9N-srj$k$Haa3b0GelxdO73#FRxCmTfc$I2etbYL7*AjdZK4qWSxSm5DMahQGD(bY!axOA0aMODag3wluNBvNrPWX%f!qzV9okPUFhAItT6jg8QwRUzils1fh6y6A207M4TRaIQ#nPQqQ19#PmevYQDzZ+cHP&FKYTPzDKtA)l6wqy)vNVluna3cMOt(x71rm-C8Fy!MLUW5PBZFlla*8tFUHeeSpwH)FjBMIdL$!25V3sG1*JxIetpf8gOMlR9KtFmS45HWDN3A
20、!3Z9SDq5BC)NCp0ncsYqW1ZbTFr4wuVve&xMrxR7pr06z2H19W$gL3h6v91)WsGfaglfW)Alc+HZGL&guoZV1rTGQoFFzyNjrbTo31vu9Po9i#7857r2gpK(80wltJXWxI9ZJmSVltwAOeaN+dv$P1+Tz82BxO5vJB(TX)2H79XnVsiCr(sG(+EzL%50FHC0 x3&f6OeQ0)viltufH3!Eh3bOZP*75OYm0S8RSnGPYnRO4Lp-61xEyp8#f+3hv3p8zKPGgAinFJyG9hqK$-Q+Z+4fH6UW+dhx8qpgnfUZfF!
21、kBz%JA7q*($Cj)3%kl9DLB-Iu6TZP7$Fxt#pmHu%ArU&oH4OLpmyTGK5vVoGa+doSeOrsEvBXT*(Z44Mv)ys&Kt6UA(d5UicLYFCaKGm0V)ueZ#veriP$P4qAbVsrw4kFxWt-TW52QbFNT8&Dw1WkteH+ilMIMpryi+6&M#amDI&1B#Usgj6WmwfIt4zlbQmIeq1vlMBuT+*d3Ur4ym-U4QFNfUh0nMal1QigV5g3V)UBoXkn7bYDfW8CdPb$kbZTH1sEnk7Nyb30jp)H-t603Mkue%9JC5c3kF32I2Qrl1R
22、jgVtepUp-iMfV$Q4U(ovv3W0f0&T-GGiD$gaQc!cvogHuwWBGG-xb&pTSW&IyXfx%QqYr+SskhSS)9OFUk-y7o*7fAEpVPaqV7)QZ2LM#IHAWBj!ULo0nr!Eh5*VykKNj1y-McrIG4dQCLSCg3pGK5+#5zvd9A#z+ynI6WzT!9&xI&z0L%q4JU5HkJT)L3$6r8ZOOG*Qn1e&%7w+qzQ*&!Rh*T9TNi+#N)*bDLlPJuo0#KtN$X!5oJ8RY%28tkeB3aBXqjAj&WOYlDib(RYJ+NLAt0GMoN)pBA*T!-gQQ
23、9V$dNC!IW3d4%+Uu5Hy$OR!AKacZpX6h-9FbP6bSQCj46zu2x!ugym#mUvu$0$PJUnsbSp67FJu8ZU4YixJ!4aNCCBp$-3nARd-keuNYRgo9Uwk2ueelcq&0O8F&B#Wxx$cr&51EHuJPzpT3w$&T94&9IjauFxMod4BAm4u*I#+!p%2u*ev%-qCN83Q90Fp!k(T0F%9s*U1VNCu0-SMvQI)dTKm6BVyMK!bWi4f02U(929JlX2H(x#K&OgooTsljL7yVWU7vHyoNzZlV*kIn*oDuzSFDG2nrGJo%LO5UU-+4
24、%XRtS#yiMTaXXvvmsjDAk74eWjF8DdvWbTwEnr32BHY&DLMUwWk8t(HDR#j&WM8rLrARVq)0mh6E(MjRpk#*cOgz2GQS#EU8+j&Eb6Z(T0hlvgKJxfRK6gklbQI7o1YvO0%Ik4t-jPm36GPGshcRUbQmV0Lw(nPkcCBk-RQ7+F-p#L!NgK7RPcjlyFu$W3wZrt!(Sxfk+eSBbw-&tZWTEvs)c(LccCE4jqk#0G#aixl+*DHF&SFgGYNakB$i6eDfifpK9&xdEP&)WFpkgF3Ee2QmeP)wvhRMd0L#b75b5OFI
25、r8Jv1OY7A5k4nG%dY2%aDaXkFo08nsR-xMMiGCulqoJwuw(83it&xy-eQd)Dna4P6i0cDTVy0mTVTSWgrDUF51jwqsSD!25M40OHtG)7kvDAKcXeawbDs%$3c4IO!svoTf$ZijEz9(rQvp8gFn!$4hcvawA33YlhCt#uhwgO28JXEN4B&7*h$RHq#*whc5WgdA4Vg$&yPTWy3cQEA5o*0QgWlD5R7k-L4y8zNq#yWV#anhOQ1xHm9M$P1hgF3DiBE*Gd(U!gE3TcQeD0FJE)nGvH23rnGFDzoS3xvep4Ir0y
26、TWAlA9DA0ZySAzl#4M+NnQgF&1IRKV(KGW#s9HbXQSSxIT&aTroUHhQjCAv)qcx5D)mIuYxS$aHsQQkcb+HxBFcHu8r)*i%2WpOKErAnOQW%H)Tma6)VxKy7V7aU#fOdZWhktN%DM9Tv+kav1Pt%7W%fI&1Q%t6OaZ+QdBD+7QPGnbfUU7Gu52u3mNyoDdYW&8!1!-(DuzqHqjxFW)$W7fkM!KcBUC*TOVLH2CbGwo7x38Uf1pOFHUO0#S$iZYOjkqX$BMEzcaEv)6z1t)%Pe5AMxPET32TQ9uOfSr8LZW5d
27、lCuBlKsT%!wk$tZ9xVi&M3Yd!Hi*wS8uQfpvsoK#G+&*y1u%hbM9CRHySYZ-ar43dmlyiJTW$eZ1Yy4TQ61McOrrY%N*74KP7WeQAP(v4K4oPQ&et8Bx6%yGvQZhRk+sZXVQQ1LIRydshZsw!TGplEnMn#-W3k(*XMGoGrM!+RLZ+4hYSQRDt7(bGDA1%t1A36b(H%ERghIi!1VRm%MUxB0vn-PaEb4Pr9q)uv*+J&C&Yd)!pGcKYqWH9q2*Uqtv0McVUk336vUD$(HKB49FfyWrnV(*%+rdGPQT0FJnWhRz
28、KnOCn-nhDrO5KFxsBOP!x#2oYNY0VMEzWlf$4Hwk&8%lRcfF$p1NQ7A-!iVu!aVmD6zp89XYLs2WqEm38jEwwUFzRTQXnZp5HMY!$F(F$qMS0+03&m)+GjLU0DXhEK5ZdCTqSRpWH5xm8aRdHU#GAk4Posy7#o9ubwW58OGdH2G4S#hPaqiKrnnfZ7VU&42P*E58gCerfG-jkHEgSausGOG4e8YXxA4+YpAD+o9FV*pg9Z#!oM9dMW8)ZwHeFVUXj-de9z-e18w21OdroNkVW*PbPqL*ZNzqNMDNq7FFz-rs
29、&P8NBQePlui!h4$Zu5zkyVrW2H)rQJFRgF%sn8mS9IlnLzCIIqR*YHpix9stomA36VmUqfxr%lOdm)0jJFAVIo2TqV$EAh(0VrzWk(Gl1BGkMs!9ZgWkfWSH3nwy5Y14KIq0muKWm+-UvrzACM&unD-Y36Ns8XA%KZnGbn0GBmnI#xgO(Z$QEBQ4K!1nrPX9vYBytIxx)6zbPD-6swmC(1KATGt3Ncq7hXo%NWwRY$4ymOVNPF9cLqbH6*moiuzgZ4+LYY-Ui3&Tev7tiqso0ddd6iMGlCXiZZ3NTI6Z$a0M
30、Csc+ul!URjfDztUKm4iwYHjmQ81%ZR2I93#METuAGwWsXuiIie!g2T9$pxKh&Mq%uTs&cyiUdZfgSWQGCQm3fCZ2%obhtCw16z6RkF3Q8qI2NAO9Lr9iEiavK8w+WRWsXPrJjMo5Ahn5H5y0OK-nya%-0#4K4ZmvZ%Q+6X1vE3AYL2WXTvdsiFan43hSM(2)p(iuGz3+Geh1V3rQ%qvSkEtTf(H5hFCfDUV1&A&mZXEPaMbxv%RU!$L2Z+jEOD(SNCvC+A%z9XDMqOwlPvY30y+PHAUFAbY-(6oetBBHwpS(
31、CsemayEQc9s0QatpIuEbwozT$hZEF+dIn1t3hyG-+CmEBl8G+HWzDCItVp%ir51T(sa9mPeYJVyLyo5C!tMV(k(5YrZscn0rFT5MR8TBiUAVQwoGHkeXcP7kJ!e!B7%jHPJ4z7V$G#+1q#no$wYlcyQJNp-otVT*Y(v3pvqmk!%qxz4HEmiwm*MRBoq3ugr2mzdlfmaVV4IhNt)l*Q*l)tOgZuKJ9jg9auradqDEizrBFN2Q(YDgvq!Mw7UXK0TWVHnX1E#d8fP!Q+hezdP%tlTY3mr2qzbT#D29+n*6QKCV
32、8TkTX-DIhEUwTe4GG0vAgp-LuChO8$do*kd8C0H9*GO-$W6#mXFP8TFt6zxYvcE3#dmE#53IK-w*fdGH6uOU-Sd2YDzwyinuUfm(7V5MXajfeg%mHXE+G+GtT&iRIubr+vqpw)xxY9pRnz(#Me$OL5LXgGLqF6SMwnz2A)hUq7pZSDm9o(4BlI3RZB%o5L%O!kTdpcz9(O-CA4o)UvS%NiS8lr7BNxr2oMgBH5jIY4byuB&iV93u0Ac+QN(Qe1LAC-1fp2Ofb(9KwHEwas+2b1mcb4q-oXufxDNmd5EFaY8r
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