关于参数方程的所有公式，急 极坐标参数方程的全部公式
\u53c2\u6570\u65b9\u7a0b\u7684\u4e3b\u8981\u516c\u5f0f\u53ca\u8fd0\u7528\u5728\u7ed9\u5b9a\u7684\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0c\u5982\u679c\u66f2\u7ebf\u4e0a\u4efb\u610f\u4e00\u70b9\u7684\u5750\u6807\uff08x\uff0cy\uff09\u90fd\u662f\u67d0\u4e2a\u53d8\u6570t\u7684\u51fd\u6570x=f(t),y=\u03c6(t)\u4e14\u5bf9\u4e8et\u7684\u6bcf\u4e00\u4e2a\u5141\u8bb8\u503c\uff0c\u7531\u65b9\u7a0b\u7ec4\u2474\u6240\u786e\u5b9a\u7684\u70b9m(x\uff0cy\uff09\u90fd\u5728\u8fd9\u6761\u66f2\u7ebf\u4e0a\uff0c\u90a3\u4e48\u65b9\u7a0b\u7ec4\u2474\u79f0\u4e3a\u8fd9\u6761\u66f2\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b\uff0c\u8054\u7cfbx\u3001y\u4e4b\u95f4\u5173\u7cfb\u7684\u53d8\u6570\u79f0\u4e3a\u53c2\u53d8\u6570\uff0c\u7b80\u79f0\u53c2\u6570\u3002\u7c7b\u4f3c\u5730\uff0c\u4e5f\u6709\u66f2\u7ebf\u7684\u6781\u5750\u6807\u53c2\u6570\u65b9\u7a0b\u03c1=f(t),\u03b8=g(t\uff09
\u5706\u7684\u53c2\u6570\u65b9\u7a0b x=a+r cos\u03b8 y=b+r sin\u03b8\uff08\u03b8\u2208 [0\uff0c2\u03c0) \uff09 (a,b) \u4e3a\u5706\u5fc3\u5750\u6807\uff0cr \u4e3a\u5706\u534a\u5f84\uff0c\u03b8 \u4e3a\u53c2\u6570\uff0c(x,y) \u4e3a\u7ecf\u8fc7\u70b9\u7684\u5750\u6807
\u692d\u5706\u7684\u53c2\u6570\u65b9\u7a0b x=a cos\u03b8\u3000 y=b sin\u03b8\uff08\u03b8\u2208[0\uff0c2\u03c0\uff09\uff09 a\u4e3a\u957f\u534a\u8f74\u957f b\u4e3a\u77ed\u534a\u8f74\u957f \u03b8\u4e3a\u53c2\u6570
\u692d\u5706
\u53cc\u66f2\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b x=a sec\u03b8 \uff08\u6b63\u5272\uff09 y=b tan\u03b8 a\u4e3a\u5b9e\u534a\u8f74\u957f b\u4e3a\u865a\u534a\u8f74\u957f \u03b8\u4e3a\u53c2\u6570
\u629b\u7269\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b x=2pt^2 y=2pt p\u8868\u793a\u7126\u70b9\u5230\u51c6\u7ebf\u7684\u8ddd\u79bb t\u4e3a\u53c2\u6570
\u76f4\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b x=x'+tcosa y=y'+tsina,x',y'\u548ca\u8868\u793a\u76f4\u7ebf\u7ecf\u8fc7\uff08x',y'\uff09\uff0c\u4e14\u503e\u659c\u89d2\u4e3aa,t\u4e3a\u53c2\u6570.
\u6216\u8005x=x'+ut\uff0c\u3000 y=y'+vt (t\u2208R)x',y'\u76f4\u7ebf\u7ecf\u8fc7\u5b9a\u70b9\uff08x',y'),u\uff0cv\u8868\u793a\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cfd=\uff08u\uff0cv\uff09
\u5706\u7684\u6e10\u5f00\u7ebfx=r(cos\u03c6+\u03c6sin\u03c6\uff09 y=r(sin\u03c6-\u03c6cos\u03c6\uff09\uff08\u03c6\u2208[0,2\u03c0\uff09\uff09 r\u4e3a\u57fa\u5706\u7684\u534a\u5f84 \u03c6\u4e3a\u53c2\u6570
\u662f\u76f4\u89d2\u5750\u6807\u548c\u6781\u5750\u6807\u8f6c\u5316\u7684\u90a3\u51e0\u4e2a\u4e48\uff1f
绛旓細3銆侀偅涔堬紝鎴戜滑鍙互寰楀埌锛歊*v=锛坸'锛坱锛塩os胃-y'锛坱锛塻in胃锛寈'锛坱锛塻in胃+y'锛坱锛塩os胃锛夛紝杩欏氨鏄鍙傛暟鏂圭▼姹傚鐨勫熀鏈叕寮忋傚畠鎻忚堪浜嗗浣曢氳繃姹傚锛屽緱鍒伴熷害鍚戦噺鐨勬柟鍚戝拰澶у皬銆傞氳繃杩欎釜鍏紡锛鎴戜滑鍙互寰楀埌鍙傛暟鏇茬嚎鐨勫垏绾夸俊鎭紝浠庤岃繘琛岃繘涓姝ョ殑鍒嗘瀽鍜岃绠椼傚弬鏁扮殑鍚箟 1銆佸弬鏁板湪鍚勭涓嶅悓鐨勯鍩熶腑...
绛旓細瀵逛簬鏍囧噯鏂圭▼鐨勫弬鏁板寲杩囩▼锛屼富瑕佹槸閫氳繃寮曞叆鏃堕棿鍙橀噺t鏉ヨ〃绀哄彉閲忕殑鍙樺寲鍏崇郴銆傝屽浜庝竴鑸柟绋嬬殑鍙傛暟鍖栬繃绋嬪垯鏇翠负澶嶆潅锛岄渶瑕佹牴鎹姏鐗╃嚎鐨勭劍鐐逛綅缃互鍙婄壒瀹氬弬鏁扮殑鍙樺寲鏉ョ‘瀹氬叾鍙傛暟鏂圭▼鐨褰㈠紡銆備笉鍚屾儏鍐典笅鐨勫弬鏁版柟绋嬮渶瑕佹牴鎹叿浣撶殑鏁板鎺ㄥ鏉ュ緱鍑猴紝涓婅堪鍏紡鍗充负瀵瑰簲鐨勭粨璁烘у叕寮忋傛帉鎻¤繖浜涘叕寮忔湁鍔╀簬鎴戜滑鏇村ソ鍦扮悊瑙...
绛旓細鏋佸潗鏍囦笌鍙傛暟鏂圭▼鍏紡鏄В鏋愬嚑浣鐨閲嶈缁勬垚閮ㄥ垎锛屽畠浠垎鍒氳繃涓嶅悓鐨勬柟寮忔弿杩板钩闈㈠唴鐨勭偣鍜屾洸绾裤傚弬鏁版柟绋嬪叕寮忓x=g(t)鍜寉=h(t)锛岄氳繃涓涓弬鏁皌鏉ヨ〃绀虹偣鐨勮建杩癸紝甯哥敤浜庣爺绌舵洸绾跨殑鎬ц川鍜屽簲鐢紝濡備綅缃叧绯诲拰寮﹂暱璁＄畻銆傝屾瀬鍧愭爣鍒欓氳繃鏋佸緞蟻鍜屾瀬瑙捨告潵瀹氫綅鐐癸紝浠ユ瀬鐐瑰拰鏋佽酱涓哄熀纭锛屽舰鎴愪竴涓嫭鐗圭殑鍧愭爣...
绛旓細鏋佸潗鏍囦笌鍙傛暟鏂圭▼鍏紡鏄細x=g(t)锛寉=h(t)锛寈=g(t),y=h(t)锛寈=g(t)锛寉=h(t) 銆傚潗鏍囩郴涓庡弬鏁版柟绋嬫槸鎴戜滑蹇呰冪殑閫変慨鍐呭銆傞氳繃瀵硅繎鍑犲勾鍏ㄥ浗鍗峰強鍚勭渷鐪熼鐨勫垎鏋愶紝鎴戜滑鍙互鍙戠幇锛岃繖閮ㄥ垎鐨勮冩煡涓昏闆嗕腑鍦ㄥ潗鏍囩郴鐨勭浉浜掕浆鍖锛屽弬鏁版柟绋銆佹瀬鍧愭爣鏂圭▼涓庢洸绾跨殑缁煎悎搴旂敤锛屽寘鎷偣涓庣洿绾跨殑浣嶇疆鍏崇郴锛岀洿绾...
绛旓細2. 鐒跺悗瀵逛竴闃跺鏁 \( \frac{dy}{dt} \) 鍏充簬 \( t \) 姹傚锛屽緱鍒 \( \frac{d^2y}{dt^2} \)銆3. 鏈鍚庯紝灏 \( \frac{d^2y}{dt^2} \) 涔樹互 \( \frac{dt}{dx} \) 寰楀埌 \( \frac{d^2y}{dx^2} \)銆傚湪浣跨敤杩欎釜鍏紡鏃讹紝闇瑕佹敞鎰忎互涓嬪嚑鐐癸細- 纭繚鍙傛暟鏂圭▼鐨褰㈠紡姝ｇ‘锛...
绛旓細鍏充簬鍦鐨勫弬鏁版柟绋嬪叕寮鎺ㄥ锛屽渾鐨勫弬鏁版柟绋嬪叕寮忚繖涓緢澶氫汉杩樹笉鐭ラ亾锛屼粖澶╂潵涓哄ぇ瀹惰В绛斾互涓婄殑闂锛岀幇鍦ㄨ鎴戜滑涓璧锋潵鐪嬬湅鍚э紒1銆(x+a)^2+(y+b)^2 = r^2 (a,b)涓哄渾蹇,r涓哄崐寰勩
绛旓細鍙傛暟鏂圭▼鐨浜岄樁瀵兼暟鍏紡鍙互琛ㄨ堪涓猴細\(\frac{dy}{dx} = \frac{d}{dt}\left(\frac{dy}{dx}\right)\)銆傝繖閲岋紝\(\frac{dy}{dx}\) 琛ㄧず瀵 \(x\) 姹鍏充簬 \(t\) 鐨勪竴闃跺鏁帮紝鑰屼簩闃跺鏁板垯鏄 \(\frac{dy}{dx}\) 鍏充簬 \(t\) 鐨勫鏁般備竴闃跺鏁版彮绀轰簡鍑芥暟鍦ㄦ煇涓鐐瑰鐨勭灛鏃跺彉鍖栫巼...
绛旓細鍙傛暟鏂圭▼鏇茬巼鍏紡锛氭洸绾鐨鏇茬巼鍙氳繃鍙傛暟鏂圭▼鏉ヨ绠椼傝鏇茬嚎涓簉(t)=(x(t),y(t))锛屽垯鏇茬巼k鐨勮绠楀叕寮忎负锛歬 = (x'(t)y''(t) - x''(t)y'(t))/((x'(t))^2 + (y'(t))^2)^(3/2)銆傚叾涓紝k琛ㄧず鏇茬巼锛寈'(t)鍜寉'(t)鍒嗗埆鏄洸绾垮湪鍙傛暟t澶勭殑鍒囩嚎鏂滅巼锛岃寈''(t)鍜寉''(t...
绛旓細a浠ｈ〃鍗婇暱杞鐨闀垮害锛宐浠ｈ〃鍗婄煭杞寸殑闀垮害锛宺琛ㄧず鍗婂緞鐨勯暱搴︺傜悊瑙鍙傛暟鏂圭▼鍏紡锛1銆佸垎鍒互鍗婄煭杞村拰鍗婇暱杞翠负鍗婂緞鍋氭き鍦嗙殑鍐呮帴鍦嗗拰澶栨帴鍦嗐2銆佹き鍦嗕笂鐨勪换鎰忎竴鐐笰涓庡唴鎺ュ渾涓婄殑A1鐐规湁鐩稿悓鐨勭旱鍧愭爣锛屼笌澶栨帴鍦嗕笂鐨凙2鐐规湁鐩稿悓鐨勬í鍧愭爣銆3銆佅嗚鏄き鍦嗗唴鎺ュ渾鎴栧鎺ュ渾鐨勫渾蹇冭锛屼笉鏄き鍦嗕笂鐨勭偣鍜屽師鐐硅繛绾夸笌X...
绛旓細鍏充簬鏋佸潗鏍囦笌鍙傛暟鏂圭▼鍏紡鐧惧害鏂囧簱锛屾瀬鍧愭爣涓庡弬鏁版柟绋嬪叕寮忚繖涓緢澶氫汉杩樹笉鐭ラ亾锛屼粖澶╂潵涓哄ぇ瀹惰В绛斾互涓鐨闂锛岀幇鍦ㄨ鎴戜滑涓璧锋潵鐪嬬湅鍚э紒1銆佹洸绾挎柟绋嬬敤鍜岃鍏紡鍐欏紑锛屽苟涓斾袱杈瑰悓涔樹互 蟻 寰 蟻^2=蟻cos胃+蟻sin胃 锛屽洜姝ゅ寲涓虹洿瑙掑潗鏍囨柟绋嬩负 x^2+y^2=x+y 銆2銆侀厤鏂瑰彲寰楀渾蹇(1/2锛1/2)锛屽崐寰 r...
