各种标准二次曲面的方程是什么?
aX^2+bY^2+cZ^2+dXY+eYZ+fZX+gX+hY+iZ+j=0绛旓細鏂圭▼z=x^2+y^2鎻忚堪浜嗕竴涓浜屾鏇查潰锛岄氬父琚О涓哄渾閿ユ洸闈㈡垨鏃嬭浆鎶涚墿闈傞鍏堬紝鎴戜滑鍙互鐪嬪埌杩欎釜鏂圭▼涓彧鏈墄鍜寉鐨勫钩鏂归」锛屽苟涓斿畠浠殑绯绘暟閮芥槸姝ｆ暟銆傝繖鎰忓懗鐫鏃犺x鍜寉鍙栦换浣曞疄鏁板硷紝瀹冧滑鐨勫钩鏂归兘鏄潪璐熸暟銆傚洜姝わ紝z鐨勫兼绘槸闈炶礋鐨勩傚叾娆★紝杩欎釜鏂圭▼娌℃湁甯告暟椤广傝繖鎰忓懗鐫z鐨勫间笉鍙楀钩绉荤殑褰卞搷锛鏇查潰鐨鏈...
绛旓細鍦ㄧ洿瑙掑潗鏍囩郴{o锛宔1,e2,e3}鍐咃紝鎴戜滑鎶婄敱涓夊厓浜屾鏂圭▼F(x,y,z)=a11x2+2a12xy+a22y2+2a13xz+2a23yz+a33z2+2b1x+2b2y+2b3z+C=0琛ㄧず鐨勬洸闈㈢О涓浜屾鏇查潰銆備竴鑸鏉ワ紝鐩寸嚎涓庝簩娆℃洸闈㈢浉浜や簬涓や釜鐐癸紱濡傛灉鐩镐氦浜庝笁涓偣浠ヤ笂锛岄偅涔堟鐩寸嚎鍏ㄩ儴鍦ㄦ洸闈笂銆傝繖鏃剁О姝ょ洿绾夸负鏇查潰鐨姣嶇嚎銆傚鏋滀簩娆℃洸闈...
绛旓細骞抽潰蟺涓婁换鎰忎竴鐐圭殑鍧愭爣閮芥弧瓒宠繖涓柟绋嬨傝屽潗鏍囨弧瓒虫柟绋嬬殑鐐归兘鍦ㄏ涓娿備簬鏄繖涓柟绋嬪氨鏄繃鐐逛笖涓庡悜閲忓瀭鐩寸殑骞抽潰蟺鐨勬柟绋锛岀О涓哄钩闈㈢殑鐐规硶寮忔柟绋嬨1銆佺偣娉曞紡鏂圭▼锛氳骞抽潰杩囦竴鐐筂锛坸yz锛夊叾娉曞悜閲忎负n={ABC}锛屽垯骞抽潰鏂圭▼涓猴細A锛坸-x锛+B(y-y锛+C(z-z锛=0銆2銆佹埅璺濆紡鏂圭▼锛氳a銆乥銆乧鍒嗗埆涓哄钩闈...
绛旓細鍦ㄨ〃2涓紝"绫诲瀷"鍒楁弿杩颁簡浜屾鏇查潰涓績鐨勫瓨鍦ㄦ儏鍐点傚鏋淚3涓嶄负闆讹紝閭ｄ箞鏇查潰鏈夊敮涓鐨勪腑蹇冿紝鎴戜滑绉板叾涓轰腑蹇冨瀷浜屾鏇查潰銆傚弽涔嬶紝閭ｄ簺娌℃湁涓績鎴栨湁澶氫腑蹇冪殑浜屾鏇查潰鍒欏睘浜庨潪涓績鍨嬨傚敖绠′笉鍙橀噺鍙互纭畾鏇查潰鐨勫舰鐘讹紝浣嗘棤娉曠洿鎺ョ‘瀹氬叾鍦ㄧ┖闂翠腑鐨勪綅缃傝纭畾浣嶇疆锛岄渶瑕侀氳繃鍧愭爣鍙樻崲銆傝嚦浜浜屾鏇查潰鐨勬爣鍑鍨鏂圭▼锛...
绛旓細1 妞悆闈㈡槸涓夌淮绌洪棿涓殑涓绉浜屾鏇查潰锛屽叾鏍囧噯鏂圭▼鍙互琛ㄧず涓猴細((x - h)^2 / a^2) + ((y - k)^2 / b^2) + ((z - l)^2 / c^2) = 1锛屽叾涓 (h, k, l) 鏄き鐞冮潰鐨勪腑蹇冪偣鍧愭爣锛宎銆乥銆乧 鍒嗗埆琛ㄧず x銆亂銆亃 杞存柟鍚戠殑鍗婂緞闀垮害銆2. 璁╂垜浠氳繃涓涓緥瀛愭潵璇︾粏瑙ｉ噴鏍囧噯鏂圭▼...
绛旓細鏇查潰鏂圭▼鏄y^2+z^2=2x銆傝鏇茬嚎鏂圭▼涓篎绛変簬0锛寉绛変簬0楗禭杞存棆杞竴鍛ㄦ墍鐢熸垚鐨勬棆杞鏇查潰鏂圭▼灏辨槸F绛変簬0楗秡杞存棆杞竴鍛ㄦ墍鐢熸垚鐨勬棆杞洸闈㈡柟绋嬪氨鏄疐姝ｈ礋sqrt绛変簬0缁曞摢涓酱鏃嬭浆锛屾柟绋嬩腑鍝釜鍙橀噺灏变笉鍙橈紝鑰屽彟涓涓彉閲忔崲涓哄墿涓嬬殑涓や釜鍙橀噺鐨勫钩鏂瑰拰鍐嶅紑鏂癸紝鏍瑰彿鍓嶈鍔犱笂姝ｈ礋鍙疯〃绀哄x寮鏂广鏇查潰鐨瀹氫箟 鏇查潰...
绛旓細瑙ｉ噴濡備笅锛氳浜屾鏇查潰鏂圭▼z=x^2+y^2涓紝鎻忚堪浜嗕笁缁寸┖闂翠腑鐐逛笌骞抽潰鍧愭爣涔嬮棿鐨勫叧绯汇傚湪杩欎釜鏂圭▼涓紝姣忎竴涓偣鍦ㄥ钩闈笂纭畾涓涓珮搴锛岃繖涓珮搴︽槸鐢辫鐐圭殑x鍧愭爣鍜寉鍧愭爣鐨勫钩鏂瑰拰鍐冲畾鐨勩傝繖绉嶆柟绋嬫墍琛ㄧず鐨勫嚑浣曞浘褰㈠叿鏈夌壒瀹氱殑褰㈢姸鐗瑰緛銆傚綋鑰冭檻鍒皒鍜寉杞存柟鍚戝彉鍖栨椂锛屽浘鍍忓湪绌洪棿涓睍寮鍛堢幇涓轰竴绉嶆洸闈傝繖涓...
绛旓細1銆佸崟鍙跺弻鏇查潰锛(x²)/(a²)+(y²)/(b²)-(z²)/(c²)=1锛屽彲浠=ctan胃, x=asec胃cos蠁, y=bsec胃sin蠁銆2銆佸弻鍙跺弻鏇查潰锛(x²)/(a²)+(y²)/(b²)-(z²)/(c²)=-1锛屽彲浠=csec胃, x=asec胃cos...
绛旓細z=x^2+y^2琛ㄧず鐨勬槸浜屾鏇查潰涓殑閿ラ潰銆傝В閲婏細閿ラ潰鏄竴绉嶇壒娈婄殑浜屾鏇查潰锛屽畠鐨勪竴鑸舰寮忓彲浠ョ敱琛ㄨ揪寮弞 = f鎻忚堪銆傚湪杩欎釜鐗瑰畾鐨勮〃杈惧紡z=x^2+y^2涓紝z浠ｈ〃楂樺害鎴栧瀭鐩村潗鏍囷紝x鍜寉浠ｈ〃姘村钩闈㈢殑鍧愭爣銆傝繖涓鏂圭▼鎻忚堪浜嗕竴涓湪涓夌淮绌洪棿涓睍寮鐨勬洸闈紝鍏朵腑姣忎竴涓偣閮芥湁涓涓笌涔嬪搴旂殑z鍊笺傚叿浣撴潵璇达紝璇...
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)锛屾墍浠ラ敟闈鐨勬柟绋嬫槸锛歾^2=(tan伪)^2(x^2+y^2).鍦浜屾鏇查潰閲岋紝妞渾闈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...
