{"id":520095,"date":"2024-10-05T11:05:08","date_gmt":"2024-10-05T03:05:08","guid":{"rendered":"https:\/\/www.youtupa.com\/gonglue\/520095.html"},"modified":"2024-10-06T02:44:18","modified_gmt":"2024-10-05T18:44:18","slug":"2024%e6%95%b0%e5%ad%a6%e6%88%90%e4%ba%ba%e9%ab%98%e8%80%83%e5%bf%85%e5%a4%87%e6%a0%b8%e5%bf%83%e7%9f%a5%e8%af%86%e7%82%b9-%e7%b2%be%e5%8d%8e%e8%80%83%e7%82%b9%e5%bd%92%e7%ba%b3","status":"publish","type":"post","link":"https:\/\/www.youtupa.com\/gonglue\/520095.html","title":{"rendered":"2024\u6570\u5b66\u6210\u4eba\u9ad8\u8003\u5fc5\u5907\u6838\u5fc3\u77e5\u8bc6\u70b9 \u7cbe\u534e\u8003\u70b9\u5f52\u7eb3"},"content":{"rendered":"
\"2024\u6570\u5b66\u6210\u4eba\u9ad8\u8003\u5fc5\u5907\u6838\u5fc3\u77e5\u8bc6\u70b9<\/figure>\n<\/p>\n

\u6210\u4eba\u9ad8\u8003\u6570\u5b66\u8003\u8bd5\u7684\u77e5\u8bc6\u70b9\u6db5\u76d6\u4e86\u57fa\u672c\u7684\u6570\u5b66\u6982\u5ff5\u548c\u6280\u80fd\u3002\u8003\u751f\u5e94\u8be5\u6df1\u5165\u7406\u89e3\u8fd9\u4e9b\u6982\u5ff5\u548c\u6280\u80fd\uff0c\u5e76\u901a\u8fc7\u89e3\u51b3\u5404\u79cd\u6570\u5b66\u95ee\u9898\u6765\u63d0\u9ad8\u6570\u5b66\u5e94\u7528\u80fd\u529b\u3002\u4ee5\u4e0b\u662f\u6570\u5b66\u6210\u4eba\u9ad8\u8003\u7684\u4e3b\u8981\u77e5\u8bc6\u70b9\u6c47\u603b\uff1a<\/p>\n

\u6210\u4eba\u9ad8\u8003\u5fc5\u8003\u6570\u5b66\u77e5\u8bc6\u70b9\u6c47\u603b<\/h2>\n

\u4e00\u3001\u51fd\u6570\u4e0e\u5bfc\u6570<\/p>\n

\u51fd\u6570\u662f\u6570\u5b66\u4e2d\u7684\u91cd\u8981\u6982\u5ff5\uff0c\u6210\u4eba\u9ad8\u8003\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u4e2d\u4e5f\u4f1a\u6d89\u53ca\u5230\u3002\u901a\u8fc7\u5b66\u4e60\u51fd\u6570\u7684\u6027\u8d28\u548c\u56fe\u50cf\uff0c\u8003\u751f\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u51fd\u6570\u7684\u5e94\u7528\u3002\u800c\u5bfc\u6570\u5219\u662f\u51fd\u6570\u7684\u91cd\u8981\u6027\u8d28\u4e4b\u4e00\uff0c\u5b83\u63cf\u8ff0\u4e86\u51fd\u6570\u5728\u67d0\u4e00\u70b9\u4e0a\u7684\u53d8\u5316\u7387\u3002\u8003\u751f\u9700\u8981\u638c\u63e1\u5bfc\u6570\u7684\u5b9a\u4e49\u3001\u6c42\u5bfc\u6cd5\u5219\u548c\u5e94\u7528\uff0c\u4f8b\u5982\u6c42\u51fd\u6570\u7684\u6781\u503c\u548c\u6700\u503c\u7b49\u3002<\/p>\n

\u4e8c\u3001\u9ad8\u4e2d\u6570\u5b66\u57fa\u7840\u77e5\u8bc6<\/p>\n

\u6210\u4eba\u9ad8\u8003\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u4e2d\uff0c\u9ad8\u4e2d\u6570\u5b66\u57fa\u7840\u77e5\u8bc6\u662f\u5fc5\u4e0d\u53ef\u5c11\u7684\u3002\u8003\u751f\u9700\u8981\u638c\u63e1\u6570\u5217\u3001\u4e09\u89d2\u51fd\u6570\u3001\u5e73\u9762\u51e0\u4f55\u3001\u7acb\u4f53\u51e0\u4f55\u7b49\u57fa\u7840\u77e5\u8bc6\u3002\u5728\u8003\u8bd5\u4e2d\uff0c\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u53ef\u80fd\u4f1a\u88ab\u878d\u5408\u5728\u4e00\u8d77\uff0c\u8003\u751f\u9700\u8981\u5177\u5907\u8f83\u5f3a\u7684\u7efc\u5408\u5206\u6790\u80fd\u529b\u3002<\/p>\n

\u4e09\u3001\u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1<\/p>\n

\u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1\u662f\u6570\u5b66\u4e2d\u7684\u4e00\u95e8\u91cd\u8981\u5206\u652f\uff0c\u4e5f\u662f\u6210\u4eba\u9ad8\u8003\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u7684\u5fc5\u8003\u70b9\u4e4b\u4e00\u3002\u8003\u751f\u9700\u8981\u638c\u63e1\u57fa\u672c\u6982\u7387\u8bba\u7684\u6982\u5ff5\u548c\u6027\u8d28\uff0c\u4f8b\u5982\u4e8b\u4ef6\u3001\u6982\u7387\u3001\u6761\u4ef6\u6982\u7387\u3001\u72ec\u7acb\u6027\u7b49\u3002\u540c\u65f6\uff0c\u8003\u751f\u8fd8\u9700\u8981\u638c\u63e1\u7edf\u8ba1\u5b66\u7684\u57fa\u672c\u6982\u5ff5\u548c\u65b9\u6cd5\uff0c\u4f8b\u5982\u6837\u672c\u3001\u603b\u4f53\u3001\u53c2\u6570\u3001\u4f30\u8ba1\u7b49\u3002<\/p>\n

\u56db\u3001\u5fae\u79ef\u5206<\/p>\n

\u5fae\u79ef\u5206\u662f\u6570\u5b66\u4e2d\u7684\u4e00\u95e8\u91cd\u8981\u5206\u652f\uff0c\u4e5f\u662f\u6210\u4eba\u9ad8\u8003\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u7684\u96be\u70b9\u4e4b\u4e00\u3002\u8003\u751f\u9700\u8981\u638c\u63e1\u5fae\u79ef\u5206\u7684\u57fa\u672c\u6982\u5ff5\u548c\u65b9\u6cd5\uff0c\u4f8b\u5982\u6781\u9650\u3001\u8fde\u7eed\u6027\u3001\u5bfc\u6570\u3001\u79ef\u5206\u7b49\u3002\u540c\u65f6\uff0c\u8003\u751f\u8fd8\u9700\u8981\u638c\u63e1\u5fae\u79ef\u5206\u7684\u5e94\u7528\uff0c\u4f8b\u5982\u66f2\u7ebf\u7684\u957f\u5ea6\u3001\u66f2\u7387\u3001\u6700\u503c\u7b49\u3002<\/p>\n

\u4e94\u3001\u7ebf\u6027\u4ee3\u6570<\/p>\n

\u7ebf\u6027\u4ee3\u6570\u662f\u6570\u5b66\u4e2d\u7684\u4e00\u95e8\u91cd\u8981\u5206\u652f\uff0c\u4e5f\u662f\u6210\u4eba\u9ad8\u8003\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u7684\u96be\u70b9\u4e4b\u4e00\u3002\u8003\u751f\u9700\u8981\u638c\u63e1\u77e9\u9635\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8fd0\u7b97\uff0c\u4f8b\u5982\u77e9\u9635\u4e58\u6cd5\u3001\u9006\u77e9\u9635\u3001\u8f6c\u7f6e\u77e9\u9635\u7b49\u3002\u540c\u65f6\uff0c\u8003\u751f\u8fd8\u9700\u8981\u638c\u63e1\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u89e3\u6cd5\u548c\u5411\u91cf\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8fd0\u7b97\u3002<\/p>\n

\u516d\u3001\u6570\u5b66\u5efa\u6a21<\/p>\n

\u6570\u5b66\u5efa\u6a21\u662f\u6570\u5b66\u4e2d\u7684\u4e00\u95e8\u91cd\u8981\u5206\u652f\uff0c\u4e5f\u662f\u6210\u4eba\u9ad8\u8003\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u7684\u96be\u70b9\u4e4b\u4e00\u3002\u8003\u751f\u9700\u8981\u638c\u63e1\u6570\u5b66\u5efa\u6a21\u7684\u57fa\u672c\u601d\u8def\u548c\u65b9\u6cd5\uff0c\u4f8b\u5982\u95ee\u9898\u5206\u6790\u3001\u5efa\u7acb\u6a21\u578b\u3001\u6c42\u89e3\u6a21\u578b\u3001\u6a21\u578b\u68c0\u9a8c\u7b49\u3002\u540c\u65f6\uff0c\u8003\u751f\u8fd8\u9700\u8981\u638c\u63e1\u4e00\u4e9b\u5e38\u89c1\u7684\u6570\u5b66\u5efa\u6a21\u65b9\u6cd5\uff0c\u4f8b\u5982\u7ebf\u6027\u89c4\u5212\u3001\u975e\u7ebf\u6027\u89c4\u5212\u3001\u52a8\u6001\u89c4\u5212\u7b49\u3002<\/p>\n

\u4e03\u3001\u6570\u5b66\u601d\u7ef4<\/p>\n

\u6570\u5b66\u601d\u7ef4\u662f\u6210\u4eba\u9ad8\u8003\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u4e2d\u7684\u91cd\u8981\u8003\u5bdf\u70b9\u4e4b\u4e00\u3002\u8003\u751f\u9700\u8981\u5177\u5907\u8f83\u5f3a\u7684\u6570\u5b66\u601d\u7ef4\u80fd\u529b\uff0c\u4f8b\u5982\u5206\u6790\u95ee\u9898\u3001\u89e3\u51b3\u95ee\u9898\u3001\u63a8\u7406\u8bba\u8bc1\u7b49\u3002\u540c\u65f6\uff0c\u8003\u751f\u8fd8\u9700\u8981\u5177\u5907\u8f83\u5f3a\u7684\u6570\u5b66\u8bed\u8a00\u8868\u8fbe\u80fd\u529b\uff0c\u4f8b\u5982\u4e25\u8c28\u7684\u8bc1\u660e\u548c\u7b80\u6d01\u7684\u53d9\u8ff0\u3002<\/p>\n

\u6210\u8003\u5fc5\u5907\u516c\u5f0f\u6709\u54ea\u4e9b<\/h2>\n

(1)\u629b\u7269\u7ebf<\/p>\n

y = ax^2 + bx + c (a\u22600)<\/p>\n

\u90a3\u662fy\u5e73\u7b49\u7684a\u4e58\u4ee5x \u52a0\u7684\u5e73\u65b9 b\u4e58\u4ee5x\u52a0 c<\/p>\n

\u653e\u7f6e\u5728\u5e73\u9762\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e2d<\/p>\n

a gt; 0\u5f00\u653e<\/p>\n

a lt; 0\u6253\u5f00<\/p>\n

(a=0\u4e00\u5143\u7ebf\u6027\u51fd\u6570)<\/p>\n

cgt;0\u65f6\u95f4\u51fd\u6570\u56fey\u8f74\u5728\u6b63\u65b9\u5411\u76f8\u4ea4<\/p>\n

clt; 0\u65f6\u95f4\u51fd\u6570\u56fey\u8f74\u5728\u8d1f\u65b9\u5411\u76f8\u4ea4<\/p>\n

c = 0\u5f53\u629b\u7269\u7ebf\u7ecf\u8fc7\u539f\u70b9\u65f6<\/p>\n

b = 0\u629b\u7269\u7ebf\u7684\u5bf9\u79f0\u8f74\u662fy\u8f74<\/p>\n

(\u5f53\u7136a=0\u548cb\u22600\u5f53\u51fd\u6570\u662f\u4e00\u6b21\u6027\u51fd\u6570\u65f6)<\/p>\n

\u8fd8\u6709\u9876\u70b9\u516c\u5f0fy = a(x+h)* 2+ k ,(h,k)=(-b\/(2a),(4ac-b^2)\/(4a))<\/p>\n

\u90a3\u662fy\u5e73\u7b49\u7684a\u4e58\u4ee5(x+h)\u5e73\u65b9+k<\/p>\n

-h\u662f\u9876\u70b9\u7684\u5750\u6807x<\/p>\n

k\u662f\u9876\u70b9\u7684\u5750\u6807y<\/p>\n

\u4e00\u822c\u7528\u4e8e\u6c42\u6700\u5927\u6700\u5c0f\u503c\u548c\u5bf9\u79f0\u8f74\u3002<\/p>\n

\u629b\u7269\u7ebf\u6807\u51c6\u65b9\u7a0b:y^2=2px<\/p>\n

\u8fd9\u610f\u5473\u7740\u629b\u7269\u7ebf\u7684\u7126\u70b9\u5728x\u5728\u6b63\u534a\u8f74\u4e0a,\u7126\u70b9\u5750\u6807\u662f(p\/2,0) \u51c6\u7ebf\u65b9\u7a0b\u662fx=-p\/2<\/p>\n

\u7531\u4e8e\u629b\u7269\u7ebf\u7684\u7126\u70b9\u53ef\u4ee5\u5728\u4efb\u610f\u534a\u8f74\u4e0a,\u6240\u4ee5\u6709\u4e00\u4e2a\u5171\u540c\u7684\u6807\u51c6\u65b9\u7a0by^2=2px y^2=-2px x^2=2py x^2=-2py<\/p>\n

(2)\u5706\u5f62\u7684<\/p>\n

\u7403\u4f53\u79ef=(4\/3)\u03c0(r^3)<\/p>\n

\u533a\u57df=\u03c0(r^2)<\/p>\n

\u5468\u957f=2\u03c0r =\u03c0d<\/p>\n

\u5706\u7684\u6807\u51c6\u65b9\u7a0b (x-a)^2+(y-b)^2=r^2 \u7b14\u8bb0\uff1a(a,b)\u662f\u5706\u5fc3\u7684\u5750\u6807<\/p>\n

\u5706\u7684\u4e00\u822c\u65b9\u7a0b x2+y2+Dx+Ey+F=0 \u7b14\u8bb0\uff1aD^2+E^2-4Fgt;0<\/p>\n

(\u4e00)\u692d\u5706\u5468\u957f\u8ba1\u7b97\u516c\u5f0f<\/p>\n

\u692d\u5706\u5468\u957f\u516c\u5f0f\uff1aL=2\u03c0b+4(a-b)<\/p>\n

\u692d\u5706\u5468\u957f\u5b9a\u7406\uff1a\u692d\u5706\u7684\u5468\u957f\u7b49\u4e8e\u4ee5\u77ed\u534a\u8f74\u4e3a\u534a\u5f84\u7684\u5706\u7684\u5468\u957f(2\u03c0b)\u52a0\u4e0a\u692d\u5706\u534a\u957f\u8f74\u957f\u5ea6\u7684\u56db\u500d(a)\u548c\u534a\u77ed\u8f74\u957f\u5ea6(b)\u533a\u522b\u3002<\/p>\n

(\u4e8c)\u692d\u5706\u9762\u79ef\u8ba1\u7b97\u516c\u5f0f<\/p>\n

\u692d\u5706\u9762\u79ef\u516c\u5f0f\uff1a S=\u03c0ab<\/p>\n

\u692d\u5706\u9762\u79ef\u5b9a\u7406\uff1a\u692d\u5706\u7684\u9762\u79ef\u7b49\u4e8epi(\u03c0)\u4e58\u4ee5\u692d\u5706\u7684\u534a\u957f\u8f74\u7684\u957f\u5ea6(a)\u548c\u534a\u77ed\u8f74\u957f\u5ea6(b)\u7684\u4ea7\u7269\u3002<\/p>\n

\u4e0a\u8ff0\u692d\u5706\u7684\u5468\u957f\u3001\u867d\u7136\u9762\u79ef\u516c\u5f0f\u4e2d\u6ca1\u6709\u692d\u5706\u663c\u591c\u6bd4T\uff0c\u4f46\u662f\u8fd9\u4e24\u4e2a\u516c\u5f0f\u90fd\u662f\u57fa\u4e8e\u692d\u5706piT\u6e90\u4e8e\u8fdb\u5316\u3002\u8eab\u4f53\u4e0d\u53d8\uff0c\u516c\u5f0f\u3002<\/p>\n

\u692d\u5706\u4f53 \u4f53\u79ef\u8ba1\u7b97\u516c\u5f0f\u692d\u5706 \u7684 \u957f\u534a\u5f84*\u77ed\u534a\u5f84*\u03c0*\u9ad8\u7684\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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