如图，这个普通方程怎么换成极坐标方程？ 普通方程通过这样变化得到的是极坐标方程吗？
\u4e00\u4e2a\u6570\u5b66\u5185\u5bb9\u3002\u8fd9\u4e2a\u666e\u901a\u65b9\u7a0b\u600e\u4e48\u5316\u4e3a\u6781\u5750\u6807\u65b9\u7a0b\uff1ax^2+y^2-2x=0\uff0c\u6c42\u8be6\u89e3\u4e0d\u662f\uff01
\u56e0\u4e3a\u9898\u76ee\u4e2d\u53ea\u80fd\u662f\u9690\u8bbe\u4e86\u76f4\u89d2\u5750\u6807\u7cfb\uff0c
\u5e76\u6ca1\u6709\u5efa\u7acb\u6781\u5750\u6807\u7cfb\uff01
\u6240\u4ee5\uff0c\u4f60\u8fd9\u91cc\u6839\u636e\u5e38\u89c4\uff0c\u53ea\u80fd\u8bf4\u662f\u4f60\u505a\u4e86
\u4e00\u79cd\u4e09\u89d2\u4ee3\u6362\uff0c\u4f46\u90fd\u8fd8\u4e0d\u77e5\u9053\u662f\u4e0d\u662f\u5408\u7406
\u7684\uff0c\u5982\u679c\u4f60\u80fd\u8bc1\u660e\u5b83\u662f\u5408\u7406\u7684\uff0c\u8003\u8bd5\u7684\u65f6\u5019\u53ef\u4ee5\u8ba4\u53ef\u6b64\u65b9\u6cd5\uff0c\u4e5f\u53ef\u4ee5\u5f97\u5230\u76f8\u5e94\u7684\u5206
\u6570\uff0c\u5982\u679c\u4e0d\u80fd\u8bf4\u660e\u5408\u7406\u6027\uff0c\u90a3\u5c31\u4e0d\u4f1a\u8ba4\u53ef
\u6b64\u65b9\u6cd5\u6709\u6548\uff0c\u4ece\u800c\u4e0d\u4f1a\u7ed9\u5206\u3002
\u6240\u4ee5\u8bf4\uff0c\u89e3\u9898\u8981\u6709\u4f9d\u636e\u624d\u884c\uff0c\u4e71\u5199
\u662f\u884c\u4e0d\u901a\u7684\u3002
带入方程：
r^2(sinθ)^2+r^2(cosθ)^2/2=1
即：r^2=2/(2（sinθ）^2+（cosθ）^2)
就是
令x=rcosθ，y=rsinθ
然后带入方程化简，就这么简单！！
绛旓細甯﹀叆鏂圭▼锛歳^2(sin胃)^2+r^2(cos胃)^2/2=1 鍗筹細r^2=2/(2锛坰in胃锛塣2+锛坈os胃锛塣2)灏辨槸 浠=rcos胃锛寉=rsin胃 鐒跺悗甯﹀叆鏂圭▼鍖栫畝锛屽氨杩欎箞绠鍗曪紒锛
绛旓細锛1锛夊厛鎶婃瀬鍧愭爣鏂圭▼涓ょ鍚屾椂涔樹互"蟻"锛屼互渚垮嚭鐜"蟻cos胃"銆"蟻sin胃"銆傜劧鍚庡垎鍒敤"x"銆"y"鏇挎崲"蟻cos胃"銆"蟻sin胃"鍚庤浆鍖栦负鐩磋鏂圭▼銆傦紙2锛夊厛鎶婃瀬鍧愭爣鏂圭▼涓よ竟鍚屾椂骞虫柟锛堟垨涔樹互"蟻^2"锛夛紝浠ヤ究鍑虹幇"蟻^2"銆傜劧鍚庯紝鎶"蟻^2"鏇挎崲鎴"x^2+y^2"鍚庤浆鍖涓烘瀬鍧愭爣鏂圭▼锛鏈鍚庯紝鍖栫畝鎴愭渶缁堢粨鏋...
绛旓細鍒╃敤鍏紡锛歺=蟻cos胃锛寉=蟻sin胃锛岀洿鎺ュ皢x鍜寉浣滀唬鎹㈠悗浠ｅ叆鍘熸柟绋嬶紝鍗冲彲灏嗙洿瑙掑潗鏍囨柟绋嬪寲涓烘瀬鍧愭爣鏂圭▼銆備緥锛歽=x²x=蟻cos胃锛寉=蟻sin胃浠ｅ叆涓婂紡寰楋細蟻sin胃=(蟻cos胃)²sin胃=蟻cos²胃 鍗充负鏋佸潗鏍囨柟绋嬨
绛旓細鍦嗙殑鏍囧噯鏂圭▼鍖栦负鏋佸潗鏍囨柟绋嬫柟娉曟槸锛灏唜=蟻cos胃锛寉=蟻sin胃甯﹀叆鍘熸柟绋嬪嵆寰楁瀬鍧愭爣鏂圭▼锛毾²cos²胃+蟻²sin²胃-a蟻cos胃+b蟻sin胃=0銆傁²(cos²胃+sin²胃)-蟻(acos胃-bsin胃)=0銆傁²-蟻(acos胃-bsin胃)=0銆傁=acos胃-bsin胃銆傝繖...
绛旓細鐩存帴灏唜鍜寉浣滃涓嬩唬鎹㈠悗锛屼唬鍏ュ師鏂圭▼锛歺=蟻cos胃锛寉=蟻sin胃锛屽嵆鍙皢鐩磋鍧愭爣鏂圭▼鍖栦负鏋佸潗鏍囨柟绋銆備緥锛歽=x²锛寈=蟻cos胃锛寉=蟻sin胃浠ｅ叆涓婂紡寰椣乻in胃=(蟻cos胃)²锛宻in胃=蟻cos²胃鍗充负鏋佸潗鏍囨柟绋嬨備竴銆佸钩闈㈠潗鏍囩郴 骞抽潰鍧愭爣绯诲湪骞抽潰鈥滀簩缁粹濆唴鐢讳袱鏉′簰鐩稿瀭鐩达紝骞朵笖鏈夊叕鍏...
绛旓細鐩磋鍧愭爣鏂圭▼鎬庝箞鍖栦负鏋佸潗鏍囨柟绋嬶紝鏈夊叕寮忓悧锛燂紙鏈夛級鐩存帴灏唜鍜寉浣滃涓嬩唬鎹㈠悗浠ｅ叆鍘熸柟绋嬶細x=蟻cos胃 y=蟻sin胃 鍗冲彲灏嗙洿瑙掑潗鏍囨柟绋嬪寲涓烘瀬鍧愭爣鏂圭▼銆備緥锛歽=x²x=蟻cos胃锛寉=蟻sin胃浠ｅ叆涓婂紡寰 蟻sin胃=锛埾乧os胃锛²sin胃=蟻cos²胃 鍗充负鏋佸潗鏍囨柟绋嬨
绛旓細胃琛ㄧず浠嶰x鍒癘M鐨勮搴︼紝蟻鍙仛鐐筂鐨勬瀬寰勶紝胃鍙仛鐐筂鐨勬瀬瑙掞紝鏈夊簭鏁板 (蟻,胃)灏卞彨鐐筂鐨勬瀬鍧愭爣锛岃繖鏍峰缓绔嬬殑鍧愭爣绯诲彨鍋氭瀬鍧愭爣绯汇傚湪鏋佸潗鏍囦腑锛寈琚乧os胃浠ｆ浛锛寉琚乻in胃浠ｆ浛銆傁=(x^2+y^2)^0.5 鍦ㄦ瀬鍧愭爣绯讳笌骞抽潰鐩磋鍧愭爣绯伙紙绗涘崱灏斿潗鏍囩郴锛(灏辨槸鍏板窞鎵璋撶殑鈥鏅氭柟绋鈥濓級闂磋浆鎹細
绛旓細蟻鍙仛鐐筂鐨勬瀬寰勶紝胃鍙仛鐐筂鐨勬瀬瑙掞紝鏈夊簭鏁板 (蟻,胃)灏卞彨鐐筂鐨勬瀬鍧愭爣锛岃繖鏍峰缓绔嬬殑鍧愭爣绯诲彨鍋氭瀬鍧愭爣绯汇傚湪鏋佸潗鏍囦腑锛寈琚 蟻cos胃 浠ｆ浛锛寉琚 蟻sin胃 浠ｆ浛銆傁=(x^2+y^2)^0.5 鍦ㄦ瀬鍧愭爣绯讳笌骞抽潰鐩磋鍧愭爣绯伙紙绗涘崱灏斿潗鏍囩郴锛(灏辨槸鍏板窞鎵璋撶殑鈥鏅氭柟绋鈥濓級闂磋浆鎹細
绛旓細3锛墆=-x+1 => rsin胃=-rcos胃+1 => r(sin胃+cos胃)=1 => r=1/(sin胃+cos胃) 锛4锛
绛旓細杩欐牱
