点P在直线L：y=x-1上
\u6c42\u8fc7\u70b9P(1,2,-1)\u548c\u76f4\u7ebfl:x-2/0=y-1/-1=z/2\u7684\u89e3\u89e3 \u8bb0A\uff081,2\uff0c-1\uff09\uff0cB\uff082,1,0\uff09
\u8bbeP\uff08x\uff0cy\uff0cz\uff09\u4e3a\u5e73\u9762\u4e0a\u4e00\u70b9
\u90a3\u4e48AP\u5411\u91cf\u548cAB\u5411\u91cf\u53ca\uff080\uff0c-1,2\uff09\u5171\u9762
\u6240\u4ee5\u53c9\u4e58\u6709|x-1 y-2 z+1|
| 1 -1 1 | =0
|0 -1 2 |
\u7b97\u8fd9\u4e2a\u884c\u5217\u5f0f\u5373\u53ef
\u8fc7\u70b9A(3\uff0c0)\uff0cB(1\uff0c1)\u7684\u76f4\u7ebfl\u7684\u76f4\u7ebf\u65b9\u7a0b\u4e3a\uff1a
y/(x-3)=1/(1-3)\uff0c \uff08\u4e24\u70b9\u5f0f\uff09
\u5373 x+2y-3=0\u3002
\u70b9P(x\uff0cy)\u76f4\u7ebfl\u4e0a\uff0c\u5373\u6ee1\u8db3\u4e0a\u65b9\u7a0b\u3002
绛旓細瑙ｏ細锛1锛夎繛鎺C锛孊C锛屸埖y=x+1涓巟杞淬亂杞村垎鍒氦浜嶢銆丅涓ょ偣锛岀偣C涓庡師鐐筄鍏充簬鐩寸嚎l瀵圭О锛庘埓OA=OB=1锛屸埓OC涓嶢B浜掔浉骞冲垎锛屼笖鍨傜洿锛岀浉绛夛紝鈭村洓杈瑰舰AOBC涓烘鏂瑰舰锛屽浜庝竴娆″嚱鏁皔=x+1锛屼护x=0锛屾眰寰锛歽=1锛涗护y=0锛屾眰寰楋細x=-1锛屸埓OA=OB=1锛屸埓A锛-1锛0锛夛紝B锛0锛1锛夛紝鈭磘an鈭燘AO=11...
绛旓細鈭 銆 璇曢鍒嗘瀽锛氾紙1锛夎繛鎺C锛孊C锛岀敱棰樻剰寰楋細鍥涜竟褰OBC涓烘鏂瑰舰锛屽浜庝竴娆″嚱鏁拌В鏋愬紡锛屽垎鍒护x涓y涓0姹傚嚭瀵逛簬y涓巟鐨勫硷紝纭畾鍑篛A涓嶰B鐨勫硷紝杩涜孋鐨勫潗鏍囷紝浠ｅ叆鍙嶆瘮渚嬭В鏋愬紡姹傚嚭k鐨勫硷紝鍗冲彲纭畾鍑哄弽姣斾緥瑙ｆ瀽寮忋傦紙2锛夎繃M浣淢E鈯杞达紝浣淣D鈯杞达紝鏍规嵁P鍦鍙嶆瘮渚嬭В鏋愬紡涓婏紝璁惧嚭P鍧愭爣寰楀嚭...
绛旓細杩欓鐩槸鑰冨ゥ鏋楀尮鍏嬮珮鎵嬬殑锛屽彧缁5鍒嗭紝澶皯浜嗗憖銆侾(a,4+a)A(x,y)鍦哋:x^2+y^2=1...(1)O(0,0),r=1 PA^2=PB^2=PO^2-r^2=a^2+(4+a)^2-1 鍦P:(x-a)^2+([y-(4+a)]^2=PA^2=PB^2=a^2+(4+a)^2-1...(2)(1)-(2):鐩寸嚎AB:ax+(4+a)y=1...(3)k...
绛旓細璁鐐筆锛坅锛宎+t锛夛紝鐐筂锛坆锛宑锛夛紝鐢遍鎰忓彲寰桺Q2=PO2-2=a2+锛坅+t锛2-2锛孭M2=锛坅-b锛2+锛坅+t-c锛2锛庣敱棰樻剰鍙緱 a2+锛坅+t锛2-2=锛坅-b锛2+锛坅+t-c锛2锛屽寲绠鍙緱锛2b+2c锛塧=b2+c2+2-2ct 瀵逛换鎰忕殑瀹炴暟a閮芥垚绔嬶紝鏁呮湁2b+2c锛0b2+c2+2?2ct锛0锛屽彲寰梩=c+1c锛宑鈮...
绛旓細瑙ｏ細锛1锛夌敱鈥滀笂鍔犱笅鍑忊濈殑鍘熷垯鍙煡锛屾妸鐩寸嚎y=x鍚戜笂骞崇Щ涓涓崟浣嶉暱搴﹀悗鎵寰楃洿绾跨殑瑙ｆ瀽寮忎负锛歽=x+1锛庢墍浠ワ紝璇ョ洿绾夸笌鍧愭爣杞寸殑浜ょ偣鏄紙0锛1锛夛紝锛-1锛0锛夛紟鍥捐薄濡傚浘鎵绀猴細锛2锛夊鍥炬墍绀猴紝鐐筆鐨勬í鍧愭爣鏄細x=4+12=2.5锛庘埖鐐筆鍦ㄧ洿绾y=x+1涓锛屸埓鐐筆鐨勭旱鍧愭爣鏄細y=2.5+1=3.5锛庘埓鈻...
绛旓細鐩寸嚎Ax+By+C=0 鍧愭爣锛圶o锛孻o锛夐偅涔堣繖鐐瑰埌杩欑洿绾跨殑璺濈灏变负锛氬叕寮忔弿杩帮細鍏紡涓殑鐩寸嚎鏂圭▼涓篈x+By+C=0锛鐐筆鐨勫潗鏍囦负(x0,y0)銆傝繛鎺ョ洿绾垮涓鐐逛笌鐩寸嚎涓鍚勭偣鐨勬墍鏈夌嚎娈典腑锛屽瀭绾挎鏈鐭紝杩欐潯鍨傜嚎娈电殑闀垮害锛屽彨鍋氱偣鍒扮洿绾跨殑璺濈銆
绛旓細閮暒椤掑洖绛旓細鐩寸嚎l锛x-y-1=0锛屽嵆y=x锛1锛屾枩鐜噆1=1锛孉B=鈭歔4²+锛4锛1锛²]=5锛岀洿绾緼B鐨勬枩鐜噆2=锛4锛1锛/锛0锛4锛=锛3/4锛孉B鐨勭洿绾挎柟绋嬫槸y=锛嶏紙3/4锛墄+4銆鐐筆浣嶄簬鐩寸嚎AB涓庣洿绾縧鐨勪氦鐐逛笂锛岃鐐筆鐨勫潗鏍囨槸P锛坸锛寉锛夛紝锛堜负鏂逛究鐪佸幓浜P鐐鐨勫潗鏍噚涓巠鐨勪笅鏍囷級鍒 Y ...
绛旓細鐐筆(x0,y0,z0)鍒鐩寸嚎{A1x+B1y+C1z+D1=0 A2x+B2y+C2z+D2=0 璺濈鐨勪竴涓叕寮:d=|(A1x0+B1y0+C1z0+D1)n鈫2-(A2x0+B2y0+C2z0+D2)n鈫1||n鈫1脳n鈫2|鍏朵腑n鈫抜={Ai,Bi,Ci},(i=1,2)绌洪棿鍑犱綍浣撹〃闈㈢Н璁＄畻鍏紡 1銆佺洿妫辨煴鍜屾妫遍敟鐨勮〃闈㈢Н 璁炬１鏌遍珮涓篽銆佸簳闈㈠杈瑰舰鐨...
绛旓細鐐笷(0,1)鍒鐩寸嚎L鐨勮窛绂讳负2锛屽洜涓哄渾杩嘑骞朵笖涓嶭鐩稿垏锛岃鐩村緞鏈灏忥紝鍙兘璺濈2灏辨槸鐩村緞銆傛墍浠ュ崐寰勪负1锛屽渾蹇冨湪鍘熺偣(0,0)銆傚苟涓旓紝缁忚繃璁＄畻锛屽師鐐瑰埌鐩寸嚎x-y+鈭2=0鐨勮窛绂籨=|0-0+鈭2|/鈭(1+1)=1锛屽嵆姝ゅ渾涔熷拰鐩寸嚎x-y+鈭2=0鐩稿垏浜庣偣(-鈭2/2,鈭2/2)锛岃繖灏辨槸P鐨勫潗鏍囥傛墍浠ワ紝褰撳渾闈㈢Н...
绛旓細鎴戝垎鍒妇渚嬪瓙鏉ュ洖绛旓細鐐筆锛2锛3锛夈丮锛1锛-3锛鐩寸嚎L锛2X+y=7锛涒憼 绗竴锛氬皢璇ョ偣P浠ｅ叆鐩寸嚎鏂圭▼锛氬彲鐭ラ亾2X2+3=7=7锛屽洜姝P鍦ㄧ洿绾夸笂锛涘浜嶮鐐癸紝2X1-3=-1鈮7,锛屾晠M涓嶅湪鐩寸嚎涓娿傜浜岀锛氳繃P锛2锛3锛夊缓绔嬩竴鏉＄洿绾匡紝涓轰簡鏂逛究鎴戜滑鍙栫洿绾跨殑鏂滅巼涓猴細K=1锛涘垯鏈夛細杩欐潯鐩寸嚎y=X+1锛涒憽 鑱旂珛...
