高中数学选修4-2知识点 跪求高中数学选修4-1知识点总结
\u9ad8\u4e2d\u6570\u5b66\u9009\u4fee4-2\u77e5\u8bc6\u70b9\u77e9\u9635\u4e0e\u53d8\u6362\uff1a
1\uff0e\u5df2\u77e5\u25b3ABC\uff0cA(\uff0d1\uff0c0)\uff0cB(3\uff0c0)\uff0cC(2\uff0c1)\uff0c\u5bf9\u5b83\u5148\u4f5c\u5173\u4e8ex\u8f74\u7684\u53cd\u5c04\u53d8\u6362\uff0c\u518d\u5c06\u6240\u5f97\u56fe\u5f62\u7ed5\u539f\u70b9\u9006\u65f6\u9488\u65cb\u8f6c90\u00b0\uff0e
\uff081\uff09\u5206\u522b\u6c42\u4e24\u6b21\u53d8\u6362\u6240\u5bf9\u5e94\u7684\u77e9\u9635M1\uff0cM2\uff1b
\uff082\uff09\u6c42\u70b9C\u5728\u4e24\u6b21\u8fde\u7eed\u7684\u53d8\u6362\u4f5c\u7528\u4e0b\u6240\u5f97\u5230\u7684\u70b9\u7684\u5750\u6807\uff0e
2\uff0e\u4e8c\u9636\u77e9\u9635M\u5bf9\u5e94\u7684\u53d8\u6362\u5c06\u70b9(1\uff0c\uff0d1)\u4e0e(\uff0d2\uff0c1)\u5206\u522b\u53d8\u6362\u6210\u70b9(\uff0d1\uff0c\uff0d1)\u4e0e(0\uff0c\uff0d2)\uff0e
\uff081\uff09\u6c42\u77e9\u9635M\uff1b
\uff082\uff09\u8bbe\u76f4\u7ebfl\u5728\u53d8\u6362M\u4f5c\u7528\u4e0b\u5f97\u5230\u4e86\u76f4\u7ebfm\uff1ax\uff0dy\uff1d4\uff0c\u6c42l\u7684\u65b9\u7a0b\uff0e
3\uff0e\u8bbe\u77e9\u9635M\u7684\u7279\u5f81\u503c\u4e3a\u03bb1=3\uff0c\u03bb2=\uff0d1\uff0c\u5176\u5bf9\u5e94\u7684\u4e00\u4e2a\u7279\u5f81\u5411\u91cf\u5206\u522b\u4e3a \uff0c \uff0e\u82e5 \uff0c\u8bd5\u6c42M20 \uff0e
4\uff0e\u5df2\u77e5\u4e8c\u9636\u77e9\u9635A\u7684\u5c5e\u4e8e\u7279\u5f81\u503c\uff0d1\u7684\u4e00\u4e2a\u7279\u5f81\u5411\u91cf\u4e3a \uff0c\u5c5e\u4e8e\u7279\u5f81\u503c3\u7684\u4e00\u4e2a\u7279\u5f81\u5411\u91cf\u4e3a \uff0c\u6c42\u77e9\u9635A\uff0e
5\uff0e\u8fd0\u7528\u65cb\u8f6c\u53d8\u6362\u77e9\u9635\uff0e\u6c42\u66f2\u7ebfxy\uff1d3\u7ed5\u539f\u70b9\u987a\u65f6\u9488\u65cb\u8f6c45\u00b0\u89d2\u540e\u6240\u5f97\u7684\u66f2\u7ebf\u65b9\u7a0b\uff0e
6\uff0e\uff081\uff09\u6c42\u77e9\u9635A=2312 \u7684\u9006\u77e9\u9635\uff1b \uff082\uff09\u5229\u7528\u9006\u77e9\u9635\u77e5\u8bc6\u89e3\u65b9\u7a0b\u7ec42x\uff0b3y\uff0d1\uff1d0x\uff0b2y\uff0d3\uff1d0 \uff0e
\u6781\u5750\u6807\u4e0e\u53c2\u6570\u65b9\u7a0b\uff1a
1\uff0e\u2299O1\u548c\u2299O2\u7684\u6781\u5750\u6807\u65b9\u7a0b\u5206\u522b\u4e3a \uff0e
\uff081\uff09\u628a\u2299O1\u548c\u2299O2\u7684\u6781\u5750\u6807\u65b9\u7a0b\u5316\u4e3a\u76f4\u89d2\u5750\u6807\u65b9\u7a0b\uff1b
\uff082\uff09\u6c42\u7ecf\u8fc7\u2299O1\uff0c\u2299O2\u4ea4\u70b9\u7684\u76f4\u7ebf\u7684\u76f4\u89d2\u5750\u6807\u65b9\u7a0b\uff0e
2\uff0e\u6c42\u76f4\u7ebf \u88ab\u5706 \u622a\u5f97\u7684\u5f26\u957f\uff0e
3\uff0e\u5728\u6781\u5750\u6807\u7cfb\u4e2d\uff0c\u76f4\u7ebf \u7684\u65b9\u7a0b\u4e3a \uff0c\u6c42\u70b9 \u5230\u76f4\u7ebf \u7684\u8ddd\u79bb\uff0e
4\uff0e\u5df2\u77e5\u76f4\u7ebf \u7684\u53c2\u6570\u65b9\u7a0b\uff1a \uff08 \u4e3a\u53c2\u6570\uff09\u548c\u5706 \u7684\u6781\u5750\u6807\u65b9\u7a0b\uff1a \uff0e
\uff081\uff09\u5c06\u76f4\u7ebf \u7684\u53c2\u6570\u65b9\u7a0b\u5316\u4e3a\u666e\u901a\u65b9\u7a0b\uff0c\u2299C\u7684\u6781\u5750\u6807\u65b9\u7a0b\u5316\u4e3a\u76f4\u89d2\u5750\u6807\u65b9\u7a0b\uff1b
\uff082\uff09\u5224\u65ad\u76f4\u7ebf \u548c\u2299C\u7684\u4f4d\u7f6e\u5173\u7cfb\uff0e
5\uff0e\u5df2\u77e5\u692d\u5706 \u7684\u6781\u5750\u6807\u65b9\u7a0b\u4e3a \uff0c\u70b9 \uff0c \u4e3a\u5176\u5de6\uff0c\u53f3\u7126\u70b9\uff0c\u76f4\u7ebf \u7684\u53c2\u6570\u65b9\u7a0b\u4e3a \uff0e
\uff081\uff09\u6c42\u76f4\u7ebfl\u548c\u66f2\u7ebfC\u7684\u666e\u901a\u65b9\u7a0b\uff1b
\uff082\uff09\u6c42\u70b9 \uff0c \u5230\u76f4\u7ebf \u7684\u8ddd\u79bb\u4e4b\u548c.
6\uff0e\u5df2\u77e5M\u692d\u5706 \uff08a>b>0\uff09\u4e0a\u5728\u7b2c\u4e00\u8c61\u9650\u7684\u70b9\uff0cA\uff08a\uff0c0\uff09\u548cB\uff080\uff0cb\uff09\u662f\u692d\u5706\u7684\u4e24\u4e2a\u9876\u70b9\uff0cO\u4e3a\u539f\u70b9\uff0c\u6c42\u56db\u8fb9\u5f62MAOB\u7684\u9762\u79ef\u7684\u6700\u5927\u503c\u3002
\u77e5\u8bc6\u70b9\u603b\u7ed3
\u76f8\u4f3c\u4e09\u89d2\u5f62\u7684\u5224\u5b9a\u53ca\u6709\u5173\u6027\u8d28
\u76f8\u4f3c\u4e09\u89d2\u5f62\u7684\u5b9a\u4e49\uff1a\u5bf9\u5e94\u89d2\u76f8\u7b49\uff0c\u5bf9\u5e94\u8fb9\u6210\u6bd4\u4f8b\u7684\u4e24\u4e2a\u4e09\u89d2\u5f62\u53eb\u505a\u76f8\u4f3c\u4e09\u89d2\u5f62\u3002
\u76f8\u4f3c\u4e09\u89d2\u5f62\u7684\u9884\u5907\u5b9a\u7406\uff1a\u5982\u679c\u4e00\u6761\u76f4\u7ebf\u5e73\u884c\u4e8e\u4e09\u89d2\u5f62\u7684\u4e00\u6761\u8fb9\uff0c\u4e14\u8fd9\u6761\u76f4\u7ebf\u4e0e\u539f\u4e09\u89d2\u5f62\u7684\u4e24\u6761\u8fb9\uff08\u6216\u5176\u5ef6\u957f\u7ebf\uff09\u5206\u522b\u76f8\u4ea4\uff0c\u90a3\u4e48\u6240\u6784\u6210\u7684\u4e09\u89d2\u5f62\u4e0e\u539f\u4e09\u89d2\u5f62\u76f8\u4f3c\u3002
\u5224\u5b9a\u5b9a\u74061\uff1a\u4e24\u89d2\u5bf9\u5e94\u76f8\u7b49\uff0c\u4e24\u4e09\u89d2\u5f62\u76f8\u4f3c\u3002
\u5224\u5b9a\u5b9a\u74062\uff1a\u4e24\u8fb9\u5bf9\u5e94\u6210\u6bd4\u4f8b\u4e14\u5939\u89d2\u76f8\u7b49\uff0c\u4e24\u4e09\u89d2\u5f62\u76f8\u4f3c\u3002
\u5224\u5b9a\u5b9a\u74063\uff1a\u4e09\u8fb9\u5bf9\u5e94\u6210\u6bd4\u4f8b\uff0c\u4e24\u4e09\u89d2\u5f62\u76f8\u4f3c\u3002
\u76f4\u89d2\u4e09\u89d2\u5f62\u76f8\u4f3c\u7684\u5224\u5b9a\u5b9a\u7406\uff1a\u659c\u8fb9\u548c\u4e00\u6761\u76f4\u89d2\u8fb9\u5bf9\u5e94\u6210\u6bd4\u4f8b\uff0c\u4e24\u76f4\u89d2\u4e09\u89d2\u5f62\u76f8\u4f3c\u3002
\u76f8\u4f3c\u4e09\u89d2\u5f62\u7684\u6027\u8d28\uff1a
\u76f8\u4f3c\u4e09\u89d2\u5f62\u5bf9\u5e94\u89d2\u76f8\u7b49\uff0c\u5bf9\u5e94\u8fb9\u6210\u6bd4\u4f8b
\u76f8\u4f3c\u4e09\u89d2\u5f62\u5177\u6709\u4f20\u9012\u6027
\u76f8\u4f3c\u4e09\u89d2\u5f62\u5bf9\u5e94\u9ad8\u7684\u6bd4\u3001\u5bf9\u5e94\u4e2d\u7ebf\u7684\u6bd4\u548c\u5bf9\u5e94\u89d2\u5e73\u5206\u7ebf\u7684\u6bd4\u90fd\u7b49\u4e8e\u76f8\u4f3c\u6bd4
\u76f8\u4f3c\u4e09\u89d2\u5f62\u5468\u957f\u7684\u6bd4\u7b49\u4e8e\u76f8\u4f3c\u6bd4
\u76f8\u4f3c\u4e09\u89d2\u5f62\u9762\u79ef\u6bd4\u7b49\u4e8e\u76f8\u4f3c\u6bd4\u7684\u5e73\u65b9
\u76f4\u7ebf\u548c\u5706\u7684\u4f4d\u7f6e\u5173\u7cfb
1.\u76f4\u7ebf\u548c\u5706\u4f4d\u7f6e\u5173\u7cfb\u7684\u5224\u5b9a\u65b9\u6cd5\u4e00\u662f\u65b9\u7a0b\u7684\u89c2\u70b9\uff0c\u5373\u628a\u5706\u7684\u65b9\u7a0b\u548c\u76f4\u7ebf\u7684\u65b9\u7a0b\u8054\u7acb\u6210\u65b9\u7a0b\u7ec4\uff0c\u5229\u7528\u5224\u522b\u5f0f\u0394\u6765\u8ba8\u8bba\u4f4d\u7f6e\u5173\u7cfb.
\u2460\u0394\uff1e0\uff0c\u76f4\u7ebf\u548c\u5706\u76f8\u4ea4.\u2461\u0394=0\uff0c\u76f4\u7ebf\u548c\u5706\u76f8\u5207.\u2462\u0394\uff1c0\uff0c\u76f4\u7ebf\u548c\u5706\u76f8\u79bb.
\u65b9\u6cd5\u4e8c\u662f\u51e0\u4f55\u7684\u89c2\u70b9\uff0c\u5373\u628a\u5706\u5fc3\u5230\u76f4\u7ebf\u7684\u8ddd\u79bbd\u548c\u534a\u5f84R\u7684\u5927\u5c0f\u52a0\u4ee5\u6bd4\u8f83.
\u2460d\uff1cR\uff0c\u76f4\u7ebf\u548c\u5706\u76f8\u4ea4.\u2461d=R\uff0c\u76f4\u7ebf\u548c\u5706\u76f8\u5207.\u2462d\uff1eR\uff0c\u76f4\u7ebf\u548c\u5706\u76f8\u79bb.
2.\u76f4\u7ebf\u548c\u5706\u76f8\u5207\uff0c\u8fd9\u7c7b\u95ee\u9898\u4e3b\u8981\u662f\u6c42\u5706\u7684\u5207\u7ebf\u65b9\u7a0b.\u6c42\u5706\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3b\u8981\u53ef\u5206\u4e3a\u5df2\u77e5\u659c\u7387k\u6216\u5df2\u77e5\u76f4\u7ebf\u4e0a\u4e00\u70b9\u4e24\u79cd\u60c5\u51b5\uff0c\u800c\u5df2\u77e5\u76f4\u7ebf\u4e0a\u4e00\u70b9\u53c8\u53ef\u5206\u4e3a\u5df2\u77e5\u5706\u4e0a\u4e00\u70b9\u548c\u5706\u5916\u4e00\u70b9\u4e24\u79cd\u60c5\u51b5.
3.\u76f4\u7ebf\u548c\u5706\u76f8\u4ea4\uff0c\u8fd9\u7c7b\u95ee\u9898\u4e3b\u8981\u662f\u6c42\u5f26\u957f\u4ee5\u53ca\u5f26\u7684\u4e2d\u70b9\u95ee\u9898.
\u5207\u7ebf\u7684\u6027\u8d28
\u2474\u5706\u5fc3\u5230\u5207\u7ebf\u7684\u8ddd\u79bb\u7b49\u4e8e\u5706\u7684\u534a\u5f84\uff1b\u2475\u8fc7\u5207\u70b9\u7684\u534a\u5f84\u5782\u76f4\u4e8e\u5207\u7ebf\uff1b\u2476\u7ecf\u8fc7\u5706\u5fc3\uff0c\u4e0e\u5207\u7ebf\u5782\u76f4\u7684\u76f4\u7ebf\u5fc5\u7ecf\u8fc7\u5207\u70b9\uff1b\u2477\u7ecf\u8fc7\u5207\u70b9\uff0c\u4e0e\u5207\u7ebf\u5782\u76f4\u7684\u76f4\u7ebf\u5fc5\u7ecf\u8fc7\u5706\u5fc3\uff1b\u5f53\u4e00\u6761\u76f4\u7ebf\u6ee1\u8db3\uff081\uff09\u8fc7\u5706\u5fc3\uff1b\uff082\uff09\u8fc7\u5207\u70b9\uff1b\uff083\uff09\u5782\u76f4\u4e8e\u5207\u7ebf\u4e09\u4e2a\u6027\u8d28\u4e2d\u7684\u4e24\u4e2a\u65f6\uff0c\u7b2c\u4e09\u4e2a\u6027\u8d28\u4e5f\u6ee1\u8db3.
\u5207\u7ebf\u7684\u5224\u5b9a\u5b9a\u7406
\u7ecf\u8fc7\u534a\u5f84\u7684\u5916\u7aef\u70b9\u5e76\u4e14\u5782\u76f4\u4e8e\u8fd9\u6761\u534a\u5f84\u7684\u76f4\u7ebf\u662f\u5706\u7684\u5207\u7ebf.
\u5207\u7ebf\u957f\u5b9a\u7406
\u4ece\u5706\u5916\u4e00\u70b9\u4f5c\u5706\u7684\u4e24\u6761\u5207\u7ebf\uff0c\u4e24\u5207\u7ebf\u957f\u76f8\u7b49\uff0c\u5706\u5fc3\u4e0e\u8fd9\u4e00\u70b9\u7684\u8fde\u7ebf\u5e73\u5206\u4e24\u6761\u5207\u7ebf\u7684\u5939\u89d2\uff0e
\u5706\u9525\u66f2\u7ebf\u6027\u8d28\u7684\u63a2\u8ba8
\u4e00\u3001\u5706\u9525\u66f2\u7ebf\u7684\u5b9a\u4e49
1. \u692d\u5706\uff1a\u5230\u4e24\u4e2a\u5b9a\u70b9\u7684\u8ddd\u79bb\u4e4b\u548c\u7b49\u4e8e\u5b9a\u957f\uff08\u5b9a\u957f\u5927\u4e8e\u4e24\u4e2a\u5b9a\u70b9\u95f4\u7684\u8ddd\u79bb\uff09\u7684\u52a8\u70b9\u7684\u8f68\u8ff9\u53eb\u505a\u692d\u5706\u3002\u5373\uff1a{P| |PF1|+|PF2|=2a, (2a>|F1F2|)}\u3002
2. \u53cc\u66f2\u7ebf\uff1a\u5230\u4e24\u4e2a\u5b9a\u70b9\u7684\u8ddd\u79bb\u7684\u5dee\u7684\u7edd\u5bf9\u503c\u4e3a\u5b9a\u503c\uff08\u5b9a\u503c\u5c0f\u4e8e\u4e24\u4e2a\u5b9a\u70b9\u7684\u8ddd\u79bb\uff09\u7684\u52a8\u70b9\u8f68\u8ff9\u53eb\u505a\u53cc\u66f2\u7ebf\u3002\u5373{P|||PF1|-|PF2||=2a, (2a<|F1F2|)}\u3002
3. \u5706\u9525\u66f2\u7ebf\u7684\u7edf\u4e00\u5b9a\u4e49\uff1a\u5230\u5b9a\u70b9\u7684\u8ddd\u79bb\u4e0e\u5230\u5b9a\u76f4\u7ebf\u7684\u8ddd\u79bb\u7684\u6bd4e\u662f\u5e38\u6570\u7684\u70b9\u7684\u8f68\u8ff9\u53eb\u505a\u5706\u9525\u66f2\u7ebf\u3002\u5f530\u65f6\u4e3a\u692d\u5706\uff1a\u5f53e=1\u65f6\u4e3a\u629b\u7269\u7ebf\uff1b\u5f53e>1\u65f6\u4e3a\u53cc\u66f2\u7ebf\u3002
\u4e8c\u3001\u5706\u9525\u66f2\u7ebf\u7684\u65b9\u7a0b
1.\u692d\u5706\uff1a + =1\uff08a>b>0\uff09\u6216 + =1\uff08a>b>0\uff09\uff08\u5176\u4e2d\uff0ca2=b2+c2\uff09
2.\u53cc\u66f2\u7ebf\uff1a - =1\uff08a>0, b>0\uff09\u6216 - =1\uff08a>0, b>0\uff09\uff08\u5176\u4e2d\uff0cc2=a2+b2\uff09
3.\u629b\u7269\u7ebf\uff1ay2=\u00b12px\uff08p>0\uff09\uff0cx2=\u00b12py\uff08p>0\uff09
\u4e09\u3001\u5706\u9525\u66f2\u7ebf\u7684\u6027\u8d28
1.\u692d\u5706\uff1a + =1\uff08a>b>0\uff09
\uff081\uff09\u8303\u56f4\uff1a|x|\u2264a\uff0c|y|\u2264b\uff082\uff09\u9876\u70b9\uff1a(\u00b1a,0)\uff0c(0,\u00b1b)\uff083\uff09\u7126\u70b9\uff1a(\u00b1c,0)\uff084\uff09\u79bb\u5fc3\u7387\uff1ae= \u2208(0,1)\uff085\uff09\u51c6\u7ebf\uff1ax=\u00b1
2.\u53cc\u66f2\u7ebf\uff1a - =1\uff08a>0, b>0\uff09\uff081\uff09\u8303\u56f4\uff1a|x|\u2265a, y\u2208R\uff082\uff09\u9876\u70b9\uff1a(\u00b1a,0)\uff083\uff09\u7126\u70b9\uff1a(\u00b1c,0)\uff084\uff09\u79bb\u5fc3\u7387\uff1ae= \u2208(1,+\u221e)\uff085\uff09\u51c6\u7ebf\uff1ax=\u00b1 \uff086\uff09\u6e10\u8fd1\u7ebf\uff1ay=\u00b1 x
3.\u629b\u7269\u7ebf\uff1ay2=2px(p>0)\uff081\uff09\u8303\u56f4\uff1ax\u22650, y\u2208R\uff082\uff09\u9876\u70b9\uff1a\uff080,0\uff09\uff083\uff09\u7126\u70b9\uff1a\uff08 ,0\uff09\uff084\uff09\u79bb\u5fc3\u7387\uff1ae=1\uff085\uff09\u51c6\u7ebf\uff1ax=-
\u3010\u5178\u578b\u4f8b\u9898\u3011
[\u4f8b1] \u5982\u56fe\u25b3ABC\u4e2d\uff0c\u2220C\uff0c\u2220B\u7684\u5e73\u5206\u7ebf\u76f8\u4ea4\u4e8eO\uff0c\u8fc7O\u4f5cAO\u7684\u5782\u7ebf\u4e0e\u8fb9AB\u3001AC\u5206\u522b\u4ea4\u4e8eD\u3001E\uff0c\u6c42\u8bc1\uff1a\u25b3BDO\u223d\u25b3BOC\u223d\u25b3OEC\u3002
\u8bc1\u660e\uff1a\u6613\u5f97AO\u5e73\u5206\u2220BAC\uff0cAO\u22a5DE \u2234 \u2220ADO=\u2220AEO \u2234 \u2220BDO=\u2220CEO
\u53c8\u2220BDO=90\u00b0+ \u2220BAC \u2220BOC=180\u00b0\uff0d \uff08\u2220ABC+\u2220ACB\uff09
=90\u00b0+ \u2220BAC\u2234 \u2220BDO=\u2220BOC \u53c8\u2220DBO=\u2220OBC
\u2234 \u25b3BDO\u223d\u25b3BOC \u540c\u7406\u25b3ECO\u223d\u25b3OCB\u2234 \u25b3BDO\u223d\u25b3BOC\u223d\u25b3OEC
[\u4f8b2] \u25b3ABE\u4e2d\uff0cD\u3001C\u4e3aAB\u4e0a\u4e24\u70b9\uff0cAC=AE\uff0c \uff0c\u6c42\u8bc1\uff1aEC\u5e73\u5206\u2220DEB\u3002
\u8bc1\u660e\uff1a\u2235 AE=AC \u2234 \u5373 \u53c8\u2235\u2220A=\u2220A \u2234 \u25b3EAD\u223d\u25b3BAE \u2234 \u22201=\u2220B \u2235 AE=AC
\u2234 \u22201+\u22202=\u2220ACE \u53c8\u2235\u22203+\u2220B=\u2220ACE \u2234 \u22202=\u22203\u2234 EC\u5e73\u5206\u2220DEB
[\u4f8b3] \u5df2\u77e5\uff1aD\u3001E\u5206\u522b\u5728\u25b3ABC\u7684\u8fb9AC\u548cAB\u4e0a\uff0cBD\u4e0eCE\u4ea4\u4e8eF\uff0c\u5176\u4e2dAE=BE\uff0c \uff0c \uff0c\u6c42 \u3002
\u8bc1\u660e\uff1a\u53d6AD\u4e2d\u70b9N\uff0c\u8fde\u7ed3EN \u2234 EN BD
\u2234 \u2234
\u2235 \u2234 \u00d7 = \u2235 = \u2234 = = =11
[\u4f8b4]\u5982\u56fe\uff0c\u76f4\u89d2\u68af\u5f62ABCD\u4e2d\uff0c\u2220A=\u2220B=90\u00b0\uff0cAD\u2016BC\uff0cE\u4e3aAB\u4e0a\u4e00\u70b9\uff0cDE\u5e73\u5206\u2220ADC\uff0cCE\u5e73\u5206\u2220BCD\uff0c\u4ee5AB\u4e3a\u76f4\u5f84\u7684\u5706\u4e0e\u8fb9CD\u6709\u600e\u6837\u7684\u4f4d\u7f6e\u5173\u7cfb\uff1f
\u89e3\uff1a\u4ee5AB\u4e3a\u76f4\u5f84\u7684\u5706\u4e0eCD\u662f\u76f8\u5207\u5173\u7cfb \u5982\u56fe\uff0c\u8fc7E\u4f5cEF\u22a5CD\uff0c\u5782\u8db3\u4e3aF\uff0e
\u2235\u2220A=\u2220B=90\u00b0\uff0c\u2234EA\u22a5AD\uff0cEB\u22a5BC\uff0c\u2235DE\u5e73\u5206\u2220ADC\uff0cCE\u5e73\u5206\u2220BCD\uff0c\u2234 \uff0e\u2234\u4ee5AB\u4e3a\u76f4\u5f84\u7684\u5706\u7684\u5706\u5fc3\u4e3aE\uff0c\u4e14 \uff0c\u2234\u4ee5AB\u4e3a\u76f4\u5f84\u7684\u5706\u4e0e\u8fb9CD\u76f8\u5207\uff0e
[\u4f8b5]\u5df2\u77e5\uff1a\u0394ABC\u5185\u63a5\u4e8e\u2299O\uff0c\u8fc7\u70b9A\u4f5c\u76f4\u7ebfEF.
\u2474\u5982\u56fe\u7532\uff0cAB\u4e3a\u76f4\u5f84\uff0c\u8981\u4f7f\u5f97EF\u662f\u2299O\u7684\u5207\u7ebf\uff0c\u8fd8\u9700\u6dfb\u52a0\u7684\u6761\u4ef6\u662f\uff08\u53ea\u9700\u5199\u51fa\u4e09\u79cd\u60c5\u51b5\uff09\uff1a
\u2460________\uff1b \u2461_________\uff1b\u2462_________. \u2475\u5982\u56fe\u4e59\uff0cAB\u4e3a\u975e\u76f4\u5f84\u7684\u5f26\uff0c\u2220CAE=\u2220B,\u6c42\u8bc1\uff1aEF\u662f\u2299O\u7684\u5207\u7ebf.
\u89e3\uff1a\u2474\u2460\u2220FAB=90\u00b0.\u2461\u2220B=\u2220EAC.\u2462\u2220BAE=90\u00b0.
\u2475\u8fde\u7ed3AO\u5e76\u5ef6\u957f\u4ea4\u2299O\u4e8eD,\u8fde\u7ed3CD. \u2235AD\u4e3a\u2299O\u7684\u76f4\u5f84\uff0c\u2234\u2220ACD=90\u00b0\uff0c\u2234\u2220D+\u2220CAD=90\u00b0. \u2235\u2220D=\u2220B,\u2220B=\u2220CAE,\u2234\u2220CAE+\u2220CAD=90\u00b0,\u5373OA\u22a5EF. \u53c8\u2235EF\u7ecf\u8fc7\u534a\u5f84OA\u7684\u5916\u7aefA\uff0c\u2234EF\u4e3a\u2299O\u7684\u5207\u7ebf.
[\u4f8b6]\u5982\u56fe\u6240\u793a\uff0cAB=AC\uff0c\u4ee5AB\u4e3a\u76f4\u5f84\u4f5c\u2299O\uff0c\u4ea4BC\u4e8e\u70b9D\uff0c\u4ea4AC\u4e8e\u70b9E\uff0c\u8fc7\u70b9D\u4f5c\u2299O\u7684\u5207\u7ebfDF\uff0c\u4ea4AC\u4e8eF\uff0c\u6c42\u8bc1\uff1a\uff081\uff09DF\u22a5AC\uff0c\uff082\uff09FC=FE.
\u8bc1\u660e\uff1a\uff081\uff09\u8fde\u7ed3OD\uff0cAD\uff0e\u2235 DF\u4e3a\u2299O\u7684\u5207\u7ebf\uff0c
\u2234 OD\u22a5DF\uff08\u5207\u7ebf\u7684\u6027\u8d28\u5b9a\u7406\uff09\uff0e\u53c8\u2235 AB\u4e3a\u2299O\u7684\u76f4\u5f84\uff0c\u2234 AD\u22a5BC\uff0e\u53c8\u2235 AB=AC\uff0c\u2234D\u4e3aBC\u4e2d\u70b9. \u2235O\u4e3aAB\u4e2d\u70b9\uff0c\u2234 \u2234 DF\u22a5AC\uff0e
\uff082\uff09\u8fde\u7ed3DE\uff0e\u5219\u2220DEC=\u2220B\uff08\u5706\u5185\u63a5\u56db\u8fb9\u5f62\u7684\u6027\u8d28\uff09\uff0c\u53c8\u2235 AB=AC\uff0c\u2234\u2220B=\u2220C\uff0e
\u2234\u2220DEC=\u2220C\uff0c\u2234 DE=DC\uff0e\u53c8\u2235 DF\u22a5AC\uff0c\u2234 FC=EF\uff08\u7b49\u8170\u4e09\u89d2\u5f62\u7684\u6027\u8d28\uff09
[\u4f8b7]\u5982\u56fe\uff1a\u692d\u5706 + =1\uff08a>b>0\uff09\uff0cF1\u4e3a\u5de6\u7126\u70b9\uff0cA\u3001B\u662f\u4e24\u4e2a\u9876\u70b9\uff0cP\u4e3a\u692d\u5706\u4e0a\u4e00\u70b9\uff0cPF1\u22a5x\u8f74\uff0c\u4e14PO//AB\uff0c\u6c42\u692d\u5706\u7684\u79bb\u5fc3\u7387e\u3002
\u89e3\uff1a\u8bbe\u692d\u5706\u7684\u53f3\u7126\u70b9\u4e3aF2\uff0c\u7531\u7b2c\u4e00\u5b9a\u4e49\uff1a|PF1|+|PF2|=2a, \u2235 PF1\u22a5x\u8f74\uff0c\u2234 |PF1|2+|F1F2|2=|PF2|2\uff0c \u5373(|PF2|+|PF1|)(|PF2|-|PF1|)=4c2,
\u2234 |PF1|= \u3002\u2235 PO//AB\uff0c\u2234 \u0394PF1O\u223d\u0394BOA,
\u2234 = c=b a= c, \u2234 e= = \u3002
[\u4f8b8] \u5df2\u77e5 \u3001 \u662f\u692d\u5706 \uff08 \uff09\u957f\u8f74\u7684\u4e24\u4e2a\u7aef\u70b9\uff0c \u662f\u4e0e \u5782\u76f4\u7684\u5f26\uff0e\u6c42\u76f4\u7ebf \u4e0e \u7684\u4ea4\u70b9M\u7684\u8f68\u8ff9\u65b9\u7a0b\uff0e
\u89e3 \u5982\u56fe\uff0c\u7531\u5df2\u77e5 \u8f74\uff0c\u53ef\u8bbe \u3001 \uff0e\u8bbe\u52a8\u70b9M\uff08 \uff09\uff0e\u2235 \uff08 \uff0c0\uff09\u3001 \uff08 \uff0c0\uff09\u2234 \u65b9\u7a0b\u4e3a \u65b9\u7a0b\u4e3a \u628a\u4e0a\u9762\u4e24\u4e2a\u7b49\u5f0f\u5de6\u3001\u53f3\u5206\u522b\u76f8\u4e58\uff0c\u53ef\u5f97\uff1a \u800cP \uff08 \uff09\u53c8\u5728\u692d\u5706\u4e0a\uff0c \u5373 \uff0c\u53d8\u5f62\u4e3a
\u5373 \uff0c\u4ee3\u5165\uff0c\u53ef\u5f97M\u70b9\u8f68\u8ff9\u65b9\u7a0b\u4e3a\uff1a \uff0e
[\u4f8b9] \u5df2\u77e5\u692d\u5706 \uff0cA\uff081\uff0c1\uff09\uff0c\u8fc7A\u7684\u76f4\u7ebf \u4ea4\u692d\u5706\u4e8eP\u3001Q\u4e24\u70b9\uff0c\u82e5 \uff0c\u6c42\u76f4\u7ebf \u7684\u65b9\u7a0b\uff0e
\u89e3\uff1a\u8bbeP\uff08 \uff0c \uff09\uff0cQ\uff08 \uff0c \uff09\u2235 \uff0c\u7531\u5b9a\u6bd4\u5206\u70b9\u516c\u5f0f\u5f97\uff1a \u2235 P\u3001Q\u5728\u692d\u5706\u4e0a \u2234
\u6574\u7406\u5f97 \u89e3\u5f97 \u6216
\u2234 \u76f4\u7ebfPQ\u7684\u65b9\u7a0b\u4e3a \u6216
一 线性变换与二阶矩阵
（一）几类特殊线性变换及其二阶矩阵
1．旋转变换 2．反射变换
3．伸缩变换 4．投影变换 5．切变变换
（二）变换、矩阵的相等 二 二阶矩阵与平面向量的乘法 三 线性变换的基本性质
（一）线性变换的基本性质 （二）一些重要线性变换对单位正方形区域的作用 第二讲 变换的复合与二阶矩阵的乘法
一 复合变换与二阶矩阵的乘法 二 矩阵乘法的性质 第三讲 逆变换与逆矩阵
一 逆变换与逆矩阵
1．逆变换与逆矩阵 2．逆矩阵的性质 二 二阶行列式与逆矩阵 三 逆矩阵与二元一次方程组 1．二元一次方程组的矩阵形式 2．逆矩阵与二元一次方程组 探索与发现 三阶矩阵与三阶行列式 第四讲 变换的不变量与矩阵的特征向量
一 变换的不变量——矩阵的特征向量
1．特征值与特征向量 2．特征值与特征向量的计算 二 特征向量的应用
1．Anα的简单表示 2．特征向量在实际问题中的应用
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