空间圆锥面方程表达式 圆锥面方程表达式
\u6c42\u5706\u9525\u9762\u65b9\u7a0b\u8868\u8fbe\u5f0f\u9525\u97622113\u4e0a\u4efb\u610f\u4e00\u70b9A(x,y,z)\u5411z\u8f74\u6295\u5f71\uff0c\u5782\u8db3B(0,0,z)\u3002\u25b3AOB\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u2220ABO=90\u00b0\uff0c\u2220BAO=\u03b1\u3002
tan\u2220BAO=tan\u03b1\uff1dOB/AB=|z|/\u221a(x^2+y^2)\uff0c\u6240\u4ee5\u9525\u9762\u7684\u65b9\u7a0b\u662f\uff1az^2=(tan\u03b1)^2(x^2+y^2).
\u5728\u4e8c\u6b21\u66f2\u9762\u91cc\uff0c\u692d\u5706\u9762\u3001\u53cc\u66f2\u9762\u3001\u9525\u9762\u3001\u692d\u5706\u629b\u7269\u9762\u4ee5\u53ca\u692d\u5706\u67f1\u9762\u90fd\u5177\u6709\u5706\u5f62\u622a\u7ebf\uff0c\u5982\u679c\u67d0\u4e00\u4e2a5261\u5e73\u9762\u622a\u4e8c\u6b21\u66f2\u9762\u4e8e\u4e00\u4e2a\u5706\u5468\uff0c\u5219\u6240\u6709\u5e73\u884c\u4e8e\u5b83\u7684\u5e73\u9762\u4e5f\u622a\u8be5\u66f2\u9762\u4e8e\u4e00\u4e2a\u5706\u5468\u3002
\u6269\u5c55\u8d44\u6599\uff1a\u5706\u9525\u7684\u4fa7\u9762\u79ef\uff1a\u5c06\u5706\u9525\u7684\u4fa7\u9762\u6cbf\u6bcd\u7ebf\u5c55\u5f00\uff0c\u662f\u4e00\u4e2a\u6247\u5f62,\u8fd9\u4e2a\u6247\u5f62\u7684\u5f27\u957f\u7b49\u4e8e\u5706\u9525\u5e95\u9762\u7684\u5468\u957f,\u800c\u6247\u5f62\u7684\u534a\u5f84\u7b49\u4e8e\u5706\u9525\u7684\u6bcd\u7ebf\u7684\u957f. \u5706\u9525\u7684\u4fa7\u9762\u79ef\u5c31\u662f\u5f27\u957f\u4e3a\u5706\u9525\u5e95\u9762\u7684\u5468\u957f\u00d7\u6bcd\u7ebf/2\uff1b\u6ca1\u5c55\u5f00\u65f6\u662f\u4e00\u4e2a\u66f2\u9762\u3002
\u5706\u9525\u6709\u4e00\u4e2a\u5e95\u9762\u3001\u4e00\u4e2a\u4fa7\u9762\u3001\u4e00\u4e2a\u9876\u70b9\u3001\u4e00\u6761\u9ad8\u3001\u65e0\u6570\u6761\u6bcd\u7ebf\uff0c\u4e14\u5e95\u9762\u5c55\u5f00\u56fe\u4e3a\u4e00\u5706\u5f62\uff0c\u4fa7\u9762\u5c55\u5f00\u56fe\u662f\u6247\u5f62\u3002
\u751f\u6d3b\u4e2d\u6c99\u5806\u3001\u6f0f\u6597\u3001\u5e3d\u5b50\u3001\u9640\u87ba\u3001\u6597\u7b20\u3001\u94c5\u7b14\u5934\u3001\u94bb\u5934\u3001\u94c5\u9524\u7b49\u90fd\u53ef\u4ee5\u8fd1\u4f3c\u5730\u770b\u4f5c\u5706\u9525\u3002\u5706\u9525\u5728\u65e5\u5e38\u751f\u6d3b\u4e2d\u4e5f\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u3002
xy+yz+zx=0\uff0c\u6216xy+yz-zx=0\uff0c\u6216xy-yz+zx=0\uff0c\u6216xy-yz-zx=0
\u4ee5\uff080.0.0\uff09\u4e3a\u5706\u9525\u9762\u9876\u70b9\uff081.0.0\uff09(0.1.0)(0.0.1)\u5728\u5706\u9525\u4e0a\uff0c\u7531\u4e09\u70b9\u51b3\u5b9a\u7684\u5e73\u9762x+y+z=1\u4e0e\u7403\u9762x^2+y^2+z^2=1\u7684\u4ea4\u7ebfl\u662f\u5706\u9525\u9762\u51c6\u7ebf\u3002
\u8bbe\u70b9p(x\uff0cy\uff0cz)\u662f\u5706\u9525\u9762\u4e0a\u7684\u70b9\uff0c\uff08u\uff0cv\uff0cw\uff09\u662f\u5706\u9525\u9762\u6bcd\u7ebfop\u4e0el\u7684\u4ea4\u70b9\uff0c\u5219op\u7684\u65b9\u7a0b\u4e3ax/u=y/v=z/w=1/t\uff0c\u5373u=xt\uff0cv=yt\uff0cw=zt
\u5e26\u5165\u51c6\u7ebf\u65b9\u7a0b\uff0c\u5f97\u65b9\u7a0b\u7ec4\uff08x+y+z\uff09t=1\u548c\uff08x^2+y^2+z^2\uff09t^2=1
\u6d88\u9664t\uff0c\u5f97\u5230\u5706\u9525\u9762\u65b9\u7a0bxy+yz+zx=0
\u6269\u5c55\u8d44\u6599
\u6027\u8d28\uff1a
\u4e00\u6761\u76f4\u7ebfx=a\u65b9/c\uff1b
\u5706 \u53c2\u6570\u65b9\u7a0b\uff1ax=X+rcos\u03b8 y=Y+rsin\u03b8 \u5706\u5fc3\u5750\u6807\uff08X,Y)\uff1b
\u692d\u5706 \u53c2\u6570\u65b9\u7a0b\uff1ax=acos\u03b8 y=bsin\u03b8 a>b\u65f6\u7126\u70b9\u5728x\u8f74\u4e0a\uff0c\u53cd\u4e4b\u5728 y\u8f74\u4e0a\uff1b
\u53cc\u66f2\u7ebf \u53c2\u6570\u65b9\u7a0b\uff1ax=asec\u03b8 y=btan\u03b8 \u7126\u70b9\u5728\u5e73\u884cx\u8f74\u7684\u76f4\u7ebf\u4e0a\uff08\u5c31\u662fx2\u2215a2-y2\u2215b2=1\uff09\uff1b
\u7126\u70b9\u5728\u5e73\u884cy\u8f74\u7684\u76f4\u7ebf\u4e0a\uff08\u5373y2\u2215a2-x2\u2215b2=1\uff09\uff0c\u628a\u6b63\u5207\u548c\u6b63\u5272\u4ea4\u6362\u3002
方程（equation）是指含有未知数的等式。是表示两个数学式（如两个数、函数、量、运算）之间相等关系的一种等式，使等式成立的未知数的值称为“解”或“根”。求方程的解的过程称为“解方程”。
绛旓細璁剧偣p(x锛寉锛寊)鏄渾閿ラ潰涓婄殑鐐癸紝锛坲锛寁锛寃锛夋槸鍦嗛敟闈㈡瘝绾縪p涓巐鐨勪氦鐐癸紝鍒檕p鐨勬柟绋嬩负x/u=y/v=z/w=1/t锛屽嵆u=xt锛寁=yt锛寃=zt 甯﹀叆鍑嗙嚎鏂圭▼锛屽緱鏂圭▼缁勶紙x+y+z锛塼=1鍜岋紙x^2+y^2+z^2锛塼^2=1 娑堥櫎t锛屽緱鍒鍦嗛敟闈㈡柟绋xy+yz+zx=0 ...
绛旓細鍦嗛敟闈鐨勫嚑浣曠壒鎬у彲閫氳繃鍏舵姇褰卞拰鎬ц川鏉ユ弿杩般傚湪鍦嗛敟闈笂鐨勪换鎰忕偣A(x, y, z)涓巣杞寸殑鍨傜洿鎶曞奖鐐笲(0, 0, z)鏋勬垚鐩磋涓夎褰⑩柍AOB锛屽叾涓垹ABO涓90搴︼紝鈭燘AO涓哄畾瑙捨便傚埄鐢ㄤ笁瑙掓瘮锛屾垜浠湁tan鈭燘AO = tan伪 = z / 鈭(x² + y²)銆傜敱姝ゅ緱鍑猴紝鍦嗛敟闈㈢殑鏂圭▼琛ㄨ揪寮涓猴細z² = ...
绛旓細閿ラ潰鐨勫畾鐞嗭細浠ュ師鐐逛负椤剁偣鐨閿ラ潰鏂圭▼鏄叧浜巟1锛寉1锛寊1鐨勯綈娆℃柟绋嬶紝鍙嶄箣锛屼竴涓惈x1锛寉1锛寊1鐨勯綈娆℃柟绋婩锛坸锛寉锛寊锛=0鐨勫浘褰㈡绘槸椤剁偣浣嶄簬鍘熺偣鐨勯敟闈備簨瀹炰笂璁綪锛坸₀锛寉₀锛寊₀锛夋槸鏇查潰F锛坸锛寉锛寊锛=0涓婄殑涓鐐(浣嗕笉鏄師鐐)銆傚嵆F锛坸₀锛寉₀锛寊₀锛=...
绛旓細閿ラ潰鏂圭▼鏄寚鎻忚堪涓夌淮绌洪棿涓敟闈㈠舰鐘剁殑鏁板琛ㄨ揪寮銆傚湪涓夌淮绗涘崱灏斿潗鏍囩郴锛坸, y, z锛変腑锛屼竴涓竴鑸殑浜屾閿ラ潰鏂圭▼鍙互琛ㄧず涓猴細Ax² + Ay² + Az² + 2Bxy + 2Cxz + 2Dyz + 2Ex + 2Fy + 2Gz + H = 0 鍏朵腑锛孉銆丅銆丆銆丏銆丒銆丗銆丟鍜孒鏄父鏁般傝繖涓柟绋嬪疄闄呬笂瀵瑰簲浜庝簩...
绛旓細閿ラ潰2113涓婁换鎰忎竴鐐笰(x,y,z)鍚憐杞存姇褰憋紝鍨傝冻B(0,0,z)銆傗柍AOB鏄洿瑙掍笁瑙掑舰锛屸垹ABO=90掳锛屸垹BAO=伪銆倀an鈭燘AO=tan伪锛漁B/AB=|z|/鈭(x^2+y^2)锛屾墍浠ラ敟闈㈢殑鏂圭▼鏄細z^2=(tan伪)^2(x^2+y^2).鍦ㄤ簩娆℃洸闈㈤噷锛屾き鍦嗛潰銆佸弻鏇查潰銆侀敟闈佹き鍦嗘姏鐗╅潰浠ュ強妞渾鏌遍潰閮藉叿鏈夊渾褰㈡埅绾匡紝濡傛灉鏌愪竴...
绛旓細2*pai*r*l/2+pai*r^2 杩欓噷r鎸囩殑鏄鍦嗛敟鍦伴潰鍦嗙殑鍗婂緞,l鏄瘝绾块暱搴,pai灏辨槸鍦嗗懆鐜,涓嶅ソ鎰忔濅笉浼氭墦,鐢ㄥ瓧姣嶄唬鏇夸竴涓
绛旓細閫氳繃涓涓畾鐐筕涓斾笌瀹氭洸绾縭(瀹冧笉杩囧畾鐐筕)鐩镐氦鐨勬墍鏈夌洿绾挎瀯鎴愮殑鏇查潰绉颁负閿ラ潰锛涘鏋滄瘝绾挎槸鍜屾棆杞酱鏂滀氦鐨勭洿绾匡紝閭ｄ箞褰㈡垚鐨勬棆杞潰鍙仛鍦嗛敟闈锛岃繖鏃讹紝姣嶇嚎鍜岃酱鐨勪氦鐐瑰彨鍋氬渾閿ラ潰鐨勯《鐐广傚父瑙佺殑鍦嗛敟鏇茬嚎鏂圭▼锛1銆佸渾 鏍囧噯鏂圭▼锛(x-a)^2+(y-b)^2=r^2,鍦嗗績(a,b),鍗婂緞=r>0 绂诲績鐜囷細e=0(娉ㄦ剰锛氬渾...
绛旓細閿ラ潰鏂圭▼鐨勪竴鑸琛ㄨ揪寮锛歾^2=锛坱an伪锛塣2锛坸^2+y^2锛夈傝繃瀹氱偣M鐨勫姩鐩寸嚎L娌跨潃涓鏉＄‘瀹氱殑鏇茬嚎C绉诲姩鎵褰㈡垚鐨勬洸闈㈢О涓洪敟闈傜洿绾縇绉颁负閿ラ潰鐨勭敓鎴愮洿绾匡紙姣嶇嚎锛夛紝鏇茬嚎C绉颁负鍑嗙嚎锛岃屽畾鐐筂鍙綔閿ラ潰鐨勪竴涓《鐐广傜畝杩 褰撳姩绾挎寜鐓т竴瀹氱殑瑙勫緥杩愬姩鏃讹紝褰㈡垚鐨勬洸闈㈢О涓鸿鍒欐洸闈紱褰撳姩绾夸綔涓嶈鍒欒繍鍔ㄦ椂锛屽舰鎴愮殑...
绛旓細閿ラ潰涓婁换鎰忎竴鐐笰(x,y,z)鍚憐杞存姇褰憋紝鍨傝冻B(0,0,z)銆傗柍AOB鏄洿瑙掍笁瑙掑舰锛屸垹ABO=90掳锛屸垹BAO=伪銆倀an鈭燘AO=tan伪锛漁B/AB=|z|/鈭(x^2+y^2)锛屾墍浠ラ敟闈㈢殑鏂圭▼鏄細z^2=(tan伪)^2(x^2+y^2).鍦ㄤ簩娆℃洸闈㈤噷锛屾き鍦嗛潰銆佸弻鏇查潰銆侀敟闈佹き鍦嗘姏鐗╅潰浠ュ強妞渾鏌遍潰閮藉叿鏈夊渾褰㈡埅绾裤傚鏋滄煇涓涓...
绛旓細閫夊彇鏇茬嚎涓婄殑鐐 P(胃)锛屽叾鍦ㄦ棆杞酱涓婄殑鎶曞奖璺濈淇濇寔涓嶅彉銆傜‘淇鍦嗛敟鍦伴潰涓庢棆杞酱鍨傜洿锛岃В鍑哄弬鏁颁箣闂寸殑鍏崇郴銆傛秷鍘诲弬鏁帮紝鏈缁堝緱鍒版棆杞洸闈㈢殑鏂圭▼锛屾彮绀轰簡鏇茬嚎鏃嬭浆鐨勫ゥ绉樸傛棆杞洸闈㈢殑绉樺瘑鍏紡鏄細鏃嬭浆鏇查潰鏂圭▼閫氳繃鏍瑰彿涓嬩袱杞村弬鏁扮殑骞虫柟鍜屾潵纭畾鏃嬭浆杞寸殑鏂瑰悜锛岃繖鏄嚑浣曚笘鐣屼腑鐙壒鐨勫绉颁笌骞宠 銆傛荤粨锛氫笁缁绌洪棿鐨...
