曲线C的极坐标方程为:p=4cosa,怎样化成普通方程
两边都乘以ρ,得ρ^=4ρcosα,
∴x^+y^=4x,为所求.
绛旓細锛1锛夆埖鏇茬嚎C鐨勬瀬鍧愭爣鏂圭▼鏄蟻=4cos胃锛0锛溛革紲蟺2锛夛紝鈭聪2=4蟻cos胃锛屽寲涓簒2+y2=4x锛屽嵆锛坸-2锛2+y2=4锛岀敱浜0锛溛革紲蟺2锛屸埓y=蟻sin胃锛0锛屽洜姝ゆ洸绾緾琛ㄧず鐨勪笂鍗婂渾锛庯紙2锛夎繃鐐P锛-2锛0锛変綔鍊炬枩瑙掍负伪鐨勭洿绾縧鏂圭▼涓猴細y=锛坸+2锛塼an伪锛庡綋鐩寸嚎l涓庡崐鍦嗙浉鍒囨椂锛屽渾蹇僀锛2锛0锛...
绛旓細涓句釜鍙嶄緥璇存槑涓涓嬶細濡傛瀬鍧愭爣鏂圭▼p=a锛堣繖閲宲琛ㄧず鏋佸緞锛宎琛ㄧず鏋佽锛夛紝鏄剧劧鐐癸紙鈭忥紝鈭忥級婊¤冻鏂圭▼锛岃岀偣锛-鈭忥紝0锛夊嵈涓嶆弧瓒虫柟绋嬨備絾杩欎袱涓偣鐨勫潗鏍囪〃绀虹殑鏄悓涓涓偣銆傛洿姝ｄ笅浣犻棶棰橈細鐐筽鍦ㄦ洸绾縞涓婂垯鐐筽鐨勬墍鏈夋瀬鍧愭爣婊¤冻鏇茬嚎c鐨勬瀬鍧愭爣鏂圭▼
绛旓細锛1锛夌偣 鍦ㄧ洿绾 涓婏紱锛2锛 . 璇曢鍒嗘瀽锛氭湰棰樿冩煡鏋佸潗鏍囨柟绋嬩笌鐩磋鍧愭爣鏂圭▼涔嬮棿鐨勮浆鍖栦互鍙婄洿绾夸笌鏇茬嚎鐩镐氦闂锛岃冩煡瀛︾敓鐨勮浆鍖栬兘鍔涘拰璁＄畻鑳藉姏.绗竴闂紝鍏堝埄鐢ㄦ瀬鍧愭爣鏂圭▼涓庣洿瑙掑潗鏍囨柟绋嬬殑浜掑寲鍏紡灏嗙洿绾 鐨勬瀬鍧愭爣鏂圭▼鍖栦负鐩磋鍧愭爣鏂圭▼锛屽啀灏嗙偣 鍖栦负鐩磋鍧愭爣绯讳笅鐨勭偣锛屽皢 鐨勫潗鏍囦唬鍏ョ洿绾挎柟绋...
绛旓細C 瑙ｏ細鍥犱负瑙锛氭洸绾跨殑鏋佸潗鏍囨柟绋蟻=4sin胃 鍗 蟻 2 =4蟻sin胃锛屽嵆 x 2 +y 2 =4y锛屽寲绠涓簒 2 +锛坹-2锛 2 =4锛岀偣(4锛)鐨勭洿瑙掑潗鏍囦负锛2锛2锛夊埄鐢ㄥ渾蹇冨埌鐐圭殑璺濈鐨勫钩鏂瑰噺鍘诲渾鐨勫崐寰勭殑骞虫柟锛屽氨鏄垏绾块暱鐨勫钩鏂癸紝鍙煡閫塁
绛旓細鐢卞凡鐭ハ=2,鍒檟^2+y^2=4鈥︹︹憼 璇存槑锛氬湪鏋佸潗鏍涓殑鐐笰鏈変袱涓噺锛屜佽〃绀篈鍒版瀬鐐筄鐨勮窛绂伙紝胃琛ㄧずX杞存鍗婅酱鍒癘A鎵鍦ㄧ洿绾跨殑瑙掑害锛岄涓=2,灏辨槸璇次稿彲浠ヤ换鎰忓彇锛屼笖鍔ㄧ偣A鍒版瀬鐐筄鐨勮窛绂讳负2鐨勭偣鐨勯泦鍚堛傛帴涓嬫潵灏卞ソ鍔炰簡锛屾妸x=t,y=t-2鈭2鈥︹︹憽浠ｅ叆鈶犱腑锛屽緱鍒板叧浜巘鐨勪竴鍏冧簩娆鏂圭▼锛岃В鍑簍...
绛旓細绗竴涓槸閿欑殑,绗簩涓篃鏄敊鐨 锛1锛夌偣p鍦ㄦ洸绾縞涓婂垯鐐筽鐨勬瀬鍧愭爣婊¤冻鏇茬嚎c鐨勬瀬鍧愭爣鏂圭▼.杩欎釜鏄敊鐨,鍥犱负鐐圭殑鏋佸潗鏍囦笉纭畾,姣斿 P=2cos胃 鍒欐瀬鐐瑰湪鏇茬嚎涓,鈭(0,蟺/2)婊¤冻鏂圭▼,浣嗘槸(0,0)鍚屾牱鏄瀬鐐,浣嗕笉婊¤冻鏂圭▼.锛2锛塼anA=1涓嶢=蟺\4琛ㄧず鍚屼竴鏉℃洸绾.杩欎釜閿欒鐨 鈭 tanA=1琛ㄧず鐩寸嚎,胃=...
绛旓細寰 鍖栨垚鏅氭柟绋 鈶 5鍒嗭紙2锛夋柟娉曚竴锛氭妸鐩寸嚎鍙傛暟鏂圭▼鍖栦负鏍囧噯鍙傛暟鏂圭▼ 锛 涓哄弬鏁帮級 鈶℃妸鈶′唬鍏モ憼寰楋細 鏁寸悊锛屽緱 锛岃鍏朵袱鏍逛负 锛屽垯 8鍒嗕粠鑰屽鸡闀夸负 10鍒嗘柟娉曚簩锛氭妸鐩寸嚎 鐨勫弬鏁版柟绋嬪寲涓烘櫘閫鏂圭▼涓 锛屼唬鍏 寰 6鍒嗚 涓C浜や簬 鍒 8鍒 10鍒 ...
绛旓細渚涘弬鑰冦
绛旓細鏇茬嚎C: 蟻(sin胃)^2=4cos胃, 寰 蟻^2(sin胃)^2=4蟻cos胃, 鍒 y^2=4x.鐩寸嚎l鐨勫弬鏁鏂圭▼涓 x=tcos胃. y=1+tsin胃锛屽緱 (y-1)/x=tan胃=k, 鍒 y=kx+1銆傜洿绾縧缁忚繃(1锛0)锛屽垯 0=k+1锛 寰 k=-1锛 鍒 y=1-x銆傚皢 y=1-x 浠ｅ叆 y^2=4x锛屽緱 (1-x)^2=4x, ...
绛旓細锛屾墍浠ョ洿绾 鐨勬瀬鍧愭爣鏂圭▼涓 .璇曢瑙ｆ瀽锛氾紙鈪狅級鐢 寰 锛庝粠鑰 鐨勭洿瑙掑潗鏍囨柟绋嬩负 锛屽嵆 锛 鏃讹紝 锛屾墍浠 锛 鏃讹紝 锛屾墍浠 锛庯紙鈪★級 鐐圭殑鐩磋鍧愭爣涓猴紙2锛0锛夛紝 鐐圭殑鐩磋鍧愭爣涓 锛庢墍浠 鐐圭殑鐩磋鍧愭爣涓 锛屽垯 鐐圭殑鏋佸潗鏍囦负 锛庢墍浠ョ洿绾 鐨勬瀬鍧愭爣鏂圭▼涓 锛
