直线方程五种形式及其限制条件
直线的五种方程 (1)点斜式 y-y1=k(x-x1) (直线不能与x轴垂直) (2)斜截式 y=kx+b (直线不能与x轴垂直) (3)两点式 (x-x1)/(x1-x2)=(y-y1)/(y1-y2) (直线不能与x轴垂直,也不能与y轴垂直) (4)截距式 x/a+y?b=1 (直线不能...绛旓細1. 涓鑸紡 Ax + By = C 闄愬埗鏉′欢锛氭枩鐜囧瓨鍦ㄤ笖鏈夐檺锛屼笉鍙椾换浣曠壒瀹氳搴︽垨鍧愭爣杞寸殑闄愬埗銆傚綋鐩寸嚎涓嶄笌鍧愭爣杞村钩琛屾椂锛岄氬父浣跨敤杩欑褰㈠紡銆傚叾涓紝A鍜孊涓嶅悓鏃朵负闆躲傚綋Ax涓烘埅璺濓紝By涓烘枩鐜囨椂锛屾牴鎹繖浜涘弬鏁板彲纭畾涓鏉″敮涓鐨勭洿绾裤備絾闇娉ㄦ剰鐩寸嚎鏂圭▼涓嶈冭檻鏂滅巼姝ｈ礋鏂瑰悜褰卞搷銆傚湪鏂滅巼鍜屾埅璺濇湭鐭ョ殑鎯呭喌涓嬶紝閫傚悎浣跨敤...
绛旓細鐩寸嚎鐨勪簲绉嶆柟绋 (1)鐐规枩寮 y-y1=k(x-x1) (鐩寸嚎涓嶈兘涓巟杞村瀭鐩) (2)鏂滄埅寮 y=kx+b (鐩寸嚎涓嶈兘涓巟杞村瀭鐩) (3)涓ょ偣寮 (x-x1)/(x1-x2)=(y-y1)/(y1-y2) (鐩寸嚎涓嶈兘涓巟杞村瀭鐩,涔熶笉鑳戒笌y杞村瀭鐩) (4)鎴窛寮 x/a+y?b=1 (鐩寸嚎涓嶈兘...
绛旓細鍥炵瓟锛氳娉ㄦ剰浜旂鐩寸嚎鏂圭▼鐨勪紭鐐瑰拰闄愬埗鏉′欢, 1銆傚凡鐭ヤ袱鐐规眰鐩寸嚎鏂圭▼鏃,瑕佸厛鐪嬭繖涓ょ偣妯潗鏍囨槸鍚︾浉绛,鍗崇湅鐩寸嚎鏄惁鍨傜洿x杞,鐩哥瓑鏃剁洿绾挎柟绋嬩负x=妯潗鏍,涓嶇浉绛夋椂鐢ㄤ袱鐐瑰紡鎴栦竴鑸紡 2銆傚凡鐭ユ枩鐜囧拰涓瀹氱偣鐢ㄧ偣鏂滃紡 3銆傚凡鐭ョ洿绾垮湪x銆亂杞寸殑鎴窛鐢ㄦ埅璺濆紡 4銆傚凡鐭ョ洿绾跨殑鏂滅巼鍜屽湪x杞翠笂鐨勬埅璺濈敤鏂滄埅寮忋 ...
绛旓細鏂规硶1锛屼唬鏁版硶鐩存帴璁剧偣鍧愭爣锛屾牴鎹鐩墍缁欑殑闄愬埗鏉′欢鍒楀嚭鍏崇郴寮忔眰瑙ｏ紝鐐笴(4锛3)鍒╃敤鍑犱綍娉曟槗鐭ョ偣C鏄鐩寸嚎CM鍜岀洿绾緼C鐨勪氦鐐癸紝鑱旂珛鏂圭▼缁勬眰瑙 鐩寸嚎鐨勬柟绋嬩富瑕佸涔浜旂褰㈠紡锛屽鐩寸嚎鐨勪簲绉嶅舰寮忔槸瑕佹眰鍚屽浠悊瑙ｅ苟璁板繂鍏紡鐨勶紝鏍规嵁棰樼洰鎵缁欐潯浠堕傚綋閫夊彇涓嶅悓褰㈠紡鏉ヨ繘琛屾眰瑙 鐐规枩寮忓拰鏂滄埅寮忛渶瑕佹枩鐜囧瓨鍦紝涓ょ偣...
绛旓細鐩寸嚎涓鑸紡鏂圭▼閫傜敤浜庢墍鏈夌殑浜岀淮绌洪棿鐩寸嚎銆傚畠鐨勫熀鏈舰寮忔槸Ax+By+C=0 锛圓锛孊涓嶅叏涓洪浂锛銆傚洜涓鸿繖鏍风殑鐗圭偣鐗瑰埆閫傚悎鍦ㄨ绠楁満棰嗗煙鐩寸嚎鐩稿叧璁＄畻涓敤鏉ユ弿杩扮洿绾裤傚凡鐭ョ洿绾夸笂涓ょ偣姹傜洿绾跨殑涓鑸紡鏂圭▼ 宸茬煡鐩寸嚎涓婄殑涓ょ偣P1(X1,Y1) P2(X2,Y2)锛 P1 P2涓ょ偣涓嶉噸鍚堛傚浜嶢X+BY+C=0锛氬綋x1=x2鏃讹紝鐩寸嚎鏂圭▼涓簒...
绛旓細4銆佹埅璺濆紡鏂圭▼锛氭牴鎹洿绾跨殑鎴窛鍜屾枩鐜囷紝鍙互鎺ㄥ鍑虹洿绾跨殑鎴窛寮忔柟绋嬶細y=kx+b鍏朵腑锛宬涓虹洿绾跨殑鏂滅巼锛宐涓烘埅璺濄傚皢宸茬煡鐨勪袱鐐逛唬鍏ユ柟绋嬶紝鍙互姹傚嚭b鐨勫硷紝浠庤屽緱鍒鐩寸嚎鏂圭▼銆傛暟瀛﹀湪鐢熸椿涓殑搴旂敤 1銆佺嚎鎬ц鍒掞細绾挎ц鍒掓槸涓绉嶆暟瀛︽柟娉曪紝鐢ㄤ簬鍦ㄧ粰瀹氫竴缁闄愬埗鏉′欢鐨勬儏鍐典笅锛屽鎵剧嚎鎬х洰鏍囧嚱鏁扮殑鏈澶у兼垨鏈灏忓笺
绛旓細鐩磋鍧愭爣鏂圭▼鏍囧噯寮忔寚鐨勬槸骞抽潰鐩磋鍧愭爣绯讳腑琛ㄧず鐩寸嚎鐨勪竴鑸舰寮忥紝鍏朵竴鑸舰寮忎负锛欰x + By = C 鍏朵腑锛孉銆丅銆丆涓哄疄鏁帮紝涓擜鍜孊涓嶅悓鏃朵负闆躲傝繖涓柟绋嬭〃绀轰簡鐩寸嚎鍦ㄧ洿瑙掑潗鏍囩郴涓殑涓鑸鏂圭▼褰㈠紡銆傚湪鏍囧噯寮忎腑锛孉鍜孊鍒嗗埆瀵瑰簲鐩寸嚎鐨勬枩鐜囩殑鍒嗗瓙鍜屽垎姣嶏紝C瀵瑰簲鐩寸嚎涓巠杞寸殑浜ょ偣锛堜篃灏辨槸y杞存埅璺濈殑鐩稿弽鏁帮級銆傞渶瑕...
绛旓細杩(a,0) (0,b)鎵浠鐩寸嚎鏂圭▼鏄細x/a+y/b=1 鍙堟湁鐩寸嚎杩囩偣(1,3)锛屾墍浠1/a+3/b=1 b=3a/(a-1)鍥犱负a鏄鏁存暟锛屾墍浠(a-1)=1鎴3鏃讹紝b鎵嶆槸姝ｆ暣鏁 a=2鏃禸=6锛宎=4鏃禸=4 杩欐牱鐨勭洿绾挎湁涓ゆ潯锛屽垎鍒 x/2+y/6=1锛寈/4+y/4=1 ...
绛旓細鐩寸嚎L1锛欰1x锛婤1y锛婥1=0锛涚洿绾縇2锛欰2x锛婤2y锛婥2=0 1銆佷袱鐩寸嚎鍨傜洿<<<===>>> A1A2锛婤1B2=0銆愮粷瀵逛笉浼氬嚭鐜板瑙ｆ垨婕忚В銆2銆佸钩琛<<<===>>> (A1)/(A2)=(B1)/(B2)鈮(C1)/(C2)鈶犲埄鐢ㄨ繖缁勭瓑寮忓垽鏂垨姹傚叾涓煇涓弬鏁扮殑鍊兼椂锛屼竴鑸槸鍏堜粠(A1)/(A2)=(B1)/(B2)鏉ユ眰鍑哄弬鏁扮殑鍊硷紝...
绛旓細涓鑸紡 ax+by+c=0 杩欎釜鏂圭▼鍙互閫傜敤浠讳綍鐩寸嚎,娌℃湁闄愬埗,浣嗘槸瑙ｉ濡傛灉鎾炰笂鐢ㄤ竴鑸紡鏉ユ眰鐩寸嚎鐨勬儏褰,100%鏄唬鍏ユ眰瑙ｄ簩鍏冧竴娆℃柟绋嬬粍,璁＄畻閲忔渶澶 鐩寸嚎鐨勫弬鏁鏂圭▼寮 x=x1+t y=y1+kt t鏄洿绾夸笂涓鐐筆,涓(x1,y1)褰㈡垚鏈夊悜绾挎鐨勬暟閲 涓鑸篃鍙互鍋 x=x1+at y=y1+bt (k=b/a)鏄剧劧,闄愬埗鏉′欢涔熸槸k...
