\u5706\u9525\u66f2\u7ebf\u786c\u89e3\u5b9a\u7406\uff08\u9ad8\u6548\u89e3\u9898\u5de5\u5177\uff0c\u9002\u914d\u9ad8\u4e2d\u6570\u5b66\u6559\u5b66\u4e0e\u9ad8\u8003\uff09<\/p>\n
\u4e00\u3001\u5b9a\u7406\u6838\u5fc3\u5b9a\u4f4d<\/p>\n
\u5706\u9525\u66f2\u7ebf\u786c\u89e3\u5b9a\u7406\u662f\u9488\u5bf9\u76f4\u7ebf\u4e0e\u692d\u5706\u3001\u53cc\u66f2\u7ebf\u3001\u629b\u7269\u7ebf\u8054\u7acb\u65b9\u7a0b\u7ec4\u7684\u7a0b\u5e8f\u5316\u8fd0\u7b97\u516c\u5f0f\uff0c\u901a\u8fc7\u9884\u8bbe\u53c2\u6570\u63a8\u5bfc\u901a\u7528\u7ed3\u679c\uff0c\u907f\u514d\u91cd\u590d\u5c55\u5f00\u5316\u7b80\uff0c\u6838\u5fc3\u4ef7\u503c\u5728\u4e8e\uff1a<\/p>\n
1. \u7f29\u77ed\u89e3\u6790\u51e0\u4f55\u5927\u9898\u7684\u8ba1\u7b97\u65f6\u95f4\uff08\u5c24\u5176\u9002\u7528\u4e8e\u8054\u7acb\u540e\u6c42\u5f26\u957f\u3001\u4e2d\u70b9\u3001\u659c\u7387\u3001\u9762\u79ef\u7b49\u95ee\u9898\uff09\uff1b<\/p>\n
2. \u964d\u4f4e\u8fd0\u7b97\u5931\u8bef\u7387\uff0c\u805a\u7126\u903b\u8f91\u63a8\u7406\u4e0e\u51e0\u4f55\u610f\u4e49\u5206\u6790\uff1b<\/p>\n
3. \u9002\u914d25\u7248\u8bfe\u6807\u5bf9\u201c\u76f4\u89c2\u60f3\u8c61\u201d\u201c\u6570\u5b66\u8fd0\u7b97\u201d\u6838\u5fc3\u7d20\u517b\u7684\u8981\u6c42\uff0c\u5e2e\u52a9\u5b66\u751f\u5728\u5feb\u901f\u8fd0\u7b97\u57fa\u7840\u4e0a\uff0c\u4e13\u6ce8\u56fe\u5f62\u6027\u8d28\u4e0e\u4ee3\u6570\u5173\u7cfb\u7684\u8f6c\u5316\u3002<\/p>\n
\u4e8c\u3001\u5b9a\u7406\u6838\u5fc3\u516c\u5f0f\uff08\u5206\u66f2\u7ebf\u7c7b\u578b\u5448\u73b0\uff0c\u9644\u4f7f\u7528\u6761\u4ef6\uff09<\/p>\n
\uff08\u4e00\uff09\u76f4\u7ebf\u4e0e\u692d\u5706\u8054\u7acb<\/p>\n
\u8bbe\u692d\u5706\u6807\u51c6\u65b9\u7a0b\uff1a$\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$\uff08$a > b > 0$\uff09\uff0c\u76f4\u7ebf\u65b9\u7a0b\uff1a$y = kx + m$\uff08\u659c\u7387\u5b58\u5728\uff0c\u659c\u7387\u4e0d\u5b58\u5728\u65f6\u5355\u72ec\u8ba8\u8bba$x = x_0$\uff09\u3002<\/p>\n
1. \u8054\u7acb\u5316\u7b80\u7ed3\u679c<\/p>\n
\u6d88\u53bb$y$\u5f97\uff1a$(b^2 + a^2k^2)x^2 + 2a^2kmx + a^2(m^2 – b^2) = 0$<\/p>\n
\u8bb0\u4e3a\uff1a$Ax^2 + Bx + C = 0$\uff08$A = b^2 + a^2k^2$\uff0c$B = 2a^2km$\uff0c$C = a^2(m^2 – b^2)$\uff09<\/p>\n
2. \u5173\u952e\u7ed3\u8bba<\/p>\n
– \u5224\u522b\u5f0f\uff1a$\\Delta = B^2 – 4AC = 4a^2b^2(b^2 + a^2k^2 – m^2)$\uff08\u76f4\u7ebf\u4e0e\u692d\u5706\u76f8\u4ea4$\\Leftrightarrow \\Delta > 0$\uff09\uff1b<\/p>\n
– \u97e6\u8fbe\u5b9a\u7406\uff1a$x_1 + x_2 = -\\frac{B}{A} = -\\frac{2a^2km}{b^2 + a^2k^2}$\uff0c$x_1x_2 = \\frac{C}{A} = \\frac{a^2(m^2 – b^2)}{b^2 + a^2k^2}$\uff1b<\/p>\n
– \u5f26\u957f\u516c\u5f0f\uff1a$|AB| = \\sqrt{1 + k^2} \\cdot \\frac{\\sqrt{\\Delta}}{|A|} = \\frac{2ab\\sqrt{(1 + k^2)(b^2 + a^2k^2 – m^2)}}{b^2 + a^2k^2}$\uff1b<\/p>\n
– \u4e2d\u70b9\u5750\u6807\uff1a\u5f26$AB$\u4e2d\u70b9$M(x_0, y_0)$\uff0c\u5219$x_0 = \\frac{x_1 + x_2}{2} = -\\frac{a^2km}{b^2 + a^2k^2}$\uff0c$y_0 = kx_0 + m = \\frac{b^2m}{b^2 + a^2k^2}$\uff08\u70b9\u5dee\u6cd5\u9a8c\u8bc1\u4e00\u81f4\uff09\u3002<\/p>\n
\uff08\u4e8c\uff09\u76f4\u7ebf\u4e0e\u53cc\u66f2\u7ebf\u8054\u7acb<\/p>\n
\u8bbe\u53cc\u66f2\u7ebf\u6807\u51c6\u65b9\u7a0b\uff1a$\\frac{x^2}{a^2} – \\frac{y^2}{b^2} = 1$\uff08$a > 0$\uff0c$b > 0$\uff09\uff0c\u76f4\u7ebf\u65b9\u7a0b\uff1a$y = kx + m$\u3002<\/p>\n
1. \u8054\u7acb\u5316\u7b80\u7ed3\u679c<\/p>\n
\u6d88\u53bb$y$\u5f97\uff1a$(b^2 – a^2k^2)x^2 – 2a^2kmx – a^2(m^2 + b^2) = 0$<\/p>\n
\u8bb0\u4e3a\uff1a$Ax^2 + Bx + C = 0$\uff08$A = b^2 – a^2k^2$\uff0c$B = -2a^2km$\uff0c$C = -a^2(m^2 + b^2)$\uff09<\/p>\n
2. \u5173\u952e\u7ed3\u8bba\uff08\u9700\u6ce8\u610f\u659c\u7387\u9650\u5236\uff09<\/p>\n
– \u5224\u522b\u5f0f\uff1a$\\Delta = B^2 – 4AC = 4a^2b^2(b^2 – a^2k^2 + m^2)$\uff08\u76f8\u4ea4$\\Leftrightarrow \\Delta > 0$\u4e14$A \\neq 0$\uff0c\u907f\u514d\u76f4\u7ebf\u4e0e\u6e10\u8fd1\u7ebf\u5e73\u884c\uff09\uff1b<\/p>\n
– \u97e6\u8fbe\u5b9a\u7406\uff1a$x_1 + x_2 = \\frac{2a^2km}{b^2 – a^2k^2}$\uff0c$x_1x_2 = -\\frac{a^2(m^2 + b^2)}{b^2 – a^2k^2}$\uff1b<\/p>\n
– \u5f26\u957f\u516c\u5f0f\uff1a$|AB| = \\sqrt{1 + k^2} \\cdot \\frac{\\sqrt{\\Delta}}{|A|} = \\frac{2ab\\sqrt{(1 + k^2)(b^2 – a^2k^2 + m^2)}}{|b^2 – a^2k^2|}$\uff1b<\/p>\n
– \u7279\u6b8a\u63d0\u9192\uff1a\u5f53$k = \\pm \\frac{b}{a}$\u65f6\uff0c\u76f4\u7ebf\u4e0e\u6e10\u8fd1\u7ebf\u5e73\u884c\uff0c\u65e0\u516c\u5171\u70b9\u6216\u4ec5\u6709\u4e00\u4e2a\u516c\u5171\u70b9\uff08\u975e\u76f8\u5207\uff09\uff0c\u9700\u5355\u72ec\u8ba8\u8bba\u3002<\/p>\n
\uff08\u4e09\uff09\u76f4\u7ebf\u4e0e\u629b\u7269\u7ebf\u8054\u7acb<\/p>\n
\u8bbe\u629b\u7269\u7ebf\u6807\u51c6\u65b9\u7a0b\uff1a$y^2 = 2px$\uff08$p > 0$\uff09\uff0c\u76f4\u7ebf\u65b9\u7a0b\uff1a$y = kx + m$\uff08$k = 0$\u65f6\u4e3a\u6c34\u5e73\u7ebf\uff0c\u5355\u72ec\u8ba8\u8bba\uff09\u3002<\/p>\n
1. \u8054\u7acb\u5316\u7b80\u7ed3\u679c<\/p>\n
\u6d88\u53bb$y$\u5f97\uff1a$k^2x^2 + 2(km – p)x + m^2 = 0$\uff08$k \\neq 0$\uff09\uff1b<\/p>\n
\u82e5\u76f4\u7ebf\u8fc7\u7126\u70b9$(\\frac{p}{2}, 0)$\uff0c\u53ef\u8bbe\u4e3a$x = ty + \\frac{p}{2}$\uff08\u907f\u514d\u659c\u7387\u4e0d\u5b58\u5728\u8ba8\u8bba\uff09\uff0c\u8054\u7acb\u5f97$y^2 – 2pty – p^2 = 0$\u3002<\/p>\n
2. \u5173\u952e\u7ed3\u8bba<\/p>\n
– \u5224\u522b\u5f0f\uff1a$\\Delta = 4(p – km)^2 – 4k^2m^2 = 4p(p – 2km)$\uff08\u76f8\u4ea4$\\Leftrightarrow \\Delta > 0$\uff09\uff1b<\/p>\n
– \u97e6\u8fbe\u5b9a\u7406\uff08$x = ty + \\frac{p}{2}$\u5f62\u5f0f\uff09\uff1a$y_1 + y_2 = 2pt$\uff0c$y_1y_2 = -p^2$\uff0c\u5f26\u957f$|AB| = y_1 + y_2 + p = 2p(t^2 + 1)$\uff08\u7126\u70b9\u5f26\u516c\u5f0f\uff0c\u9ad8\u9891\u8003\u70b9\uff09\u3002<\/p>\n
\u4e09\u3001\u6559\u5b66\u5e94\u7528\u7b56\u7565\uff08\u9002\u914d\u5b66\u751f\u57fa\u7840\u4e0e\u5206\u5c42\u6559\u5b66\uff09<\/p>\n
1. \u5b9a\u7406\u63a8\u5bfc\u4e0e\u7406\u89e3\uff08\u907f\u514d\u201c\u6b7b\u8bb0\u786c\u80cc\u201d\uff09<\/p>\n
– \u57fa\u7840\u8584\u5f31\u5b66\u751f\uff1a\u5148\u5e26\u9886\u63a8\u5bfc\u201c\u76f4\u7ebf\u4e0e\u692d\u5706\u8054\u7acb\u201d\u7684\u5b8c\u6574\u8fc7\u7a0b\uff08\u4ece\u6d88\u5143\u5230\u97e6\u8fbe\u5b9a\u7406\uff09\uff0c\u660e\u786e$A$\u3001$B$\u3001$C$\u7684\u6765\u6e90\uff0c\u901a\u8fc7GeoGebra\u52a8\u6001\u6f14\u793a\u201c\u76f4\u7ebf\u659c\u7387\u3001\u622a\u8ddd\u53d8\u5316\u65f6\uff0c$\\Delta$\u3001\u5f26\u957f\u7684\u53d8\u5316\u201d\uff0c\u5efa\u7acb\u76f4\u89c2\u8ba4\u77e5\uff1b<\/p>\n
– \u8fdb\u9636\u5b66\u751f\uff1a\u5bf9\u6bd4\u692d\u5706\u4e0e\u53cc\u66f2\u7ebf\u8054\u7acb\u540e\u7684\u7cfb\u6570\u5dee\u5f02\uff08\u7b26\u53f7\u53d8\u5316\uff09\uff0c\u5206\u6790\u629b\u7269\u7ebf\u201c\u8bbe\u7ebf\u6280\u5de7\u201d\u7684\u5408\u7406\u6027\uff0c\u7406\u89e3\u201c\u786c\u89e3\u5b9a\u7406\u662f\u4ee3\u6570\u8fd0\u7b97\u7684\u7b80\u5316\u603b\u7ed3\u201d\uff0c\u800c\u975e\u5b64\u7acb\u516c\u5f0f\u3002<\/p>\n
2. \u89e3\u9898\u6b65\u9aa4\u89c4\u8303\uff08\u9ad8\u8003\u5f97\u5206\u5173\u952e\uff09<\/p>\n
1. \u7b2c\u4e00\u6b65\uff1a\u660e\u786e\u66f2\u7ebf\u65b9\u7a0b\u4e0e\u76f4\u7ebf\u65b9\u7a0b\uff0c\u5224\u65ad\u76f4\u7ebf\u659c\u7387\u662f\u5426\u5b58\u5728\uff08\u5206\u7c7b\u8ba8\u8bba\uff09\uff1b<\/p>\n
2. \u7b2c\u4e8c\u6b65\uff1a\u4ee3\u5165\u786c\u89e3\u5b9a\u7406\u516c\u5f0f\uff0c\u5199\u51fa$A$\u3001$B$\u3001$C$\uff08\u6807\u6ce8\u66f2\u7ebf\u7c7b\u578b\uff0c\u907f\u514d\u6df7\u6dc6\u692d\u5706\u4e0e\u53cc\u66f2\u7ebf\u7684\u7cfb\u6570\uff09\uff1b<\/p>\n
3. \u7b2c\u4e09\u6b65\uff1a\u8ba1\u7b97$\\Delta$\uff0c\u5224\u65ad\u76f4\u7ebf\u4e0e\u66f2\u7ebf\u7684\u4f4d\u7f6e\u5173\u7cfb\uff08\u5fc5\u8981\u65f6\u5199\u53d6\u503c\u8303\u56f4\uff09\uff1b<\/p>\n
4. \u7b2c\u56db\u6b65\uff1a\u7528\u97e6\u8fbe\u5b9a\u7406\u6216\u5f26\u957f\u516c\u5f0f\u6c42\u89e3\u76ee\u6807\u91cf\uff08\u5982\u9762\u79ef\u3001\u659c\u7387\u3001\u5b9a\u70b9\u7b49\uff09\uff1b<\/p>\n
\u6613\u9519\u63d0\u9192\uff1a\u53cc\u66f2\u7ebf\u9700\u68c0\u9a8c$A \\neq 0$\uff0c\u629b\u7269\u7ebf\u7126\u70b9\u5f26\u4f18\u5148\u7528$x = ty + \\frac{p}{2}$\u8bbe\u7ebf\uff0c\u51cf\u5c11\u8fd0\u7b97\u91cf\u3002<\/p>\n
3. \u5178\u578b\u4f8b\u9898\uff08\u9ad8\u8003\u771f\u9898\u9002\u914d\uff09<\/p>\n
\u4f8b\uff082023\u5168\u56fd\u5377\u2160\uff09\u8bbe\u692d\u5706$C\uff1a\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$\uff08$a > b > 0$\uff09\u7684\u79bb\u5fc3\u7387\u4e3a$\\frac{\\sqrt{5}}{3}$\uff0c\u8fc7\u53f3\u7126\u70b9$F$\u7684\u76f4\u7ebf$l$\u4e0e$C$\u4ea4\u4e8e$A$\u3001$B$\u4e24\u70b9\uff0c\u5f53$l$\u5782\u76f4\u4e8e$x$\u8f74\u65f6\uff0c$|AB| = \\frac{16}{3}$\u3002<\/p>\n
\uff081\uff09\u6c42$C$\u7684\u65b9\u7a0b\uff1b\uff082\uff09\u8bbe$O$\u4e3a\u5750\u6807\u539f\u70b9\uff0c\u8fc7$O$\u7684\u76f4\u7ebf$m$\u4e0e$l$\u4ea4\u4e8e$P$\uff0c\u4e0e$C$\u4ea4\u4e8e$M$\u3001$N$\uff0c\u82e5$|PM| = |PN|$\uff0c\u6c42$|AB|$\u7684\u6700\u5c0f\u503c\u3002<\/p>\n
\u786c\u89e3\u5b9a\u7406\u5e94\u7528\u6b65\u9aa4<\/p>\n
\uff081\uff09\u7531\u79bb\u5fc3\u7387$e = \\frac{c}{a} = \\frac{\\sqrt{5}}{3}$\uff0c\u5f97$c = \\frac{\\sqrt{5}}{3}a$\uff0c$b^2 = a^2 – c^2 = \\frac{4}{9}a^2$\uff1b<\/p>\n
\u4ee4$x = c$\uff0c\u4ee3\u5165\u692d\u5706\u5f97$y = \\pm \\frac{b^2}{a}$\uff0c\u6545$|AB| = \\frac{2b^2}{a} = \\frac{16}{3}$\uff0c\u89e3\u5f97$a = 3$\uff0c$b = 2$\uff0c\u692d\u5706\u65b9\u7a0b\u4e3a$\\frac{x^2}{9} + \\frac{y^2}{4} = 1$\u3002<\/p>\n
\uff082\uff09\u8bbe$l\uff1ax = ty + \\sqrt{5}$\uff08\u8fc7\u7126\u70b9$F(\\sqrt{5}, 0)$\uff0c\u907f\u514d\u659c\u7387\u4e0d\u5b58\u5728\u8ba8\u8bba\uff09\uff0c\u8054\u7acb\u692d\u5706\u5f97\uff1a<\/p>\n
$(4t^2 + 9)y^2 + 8\\sqrt{5}ty – 16 = 0$\uff0c$\\Delta = (8\\sqrt{5}t)^2 + 4 \\times 16(4t^2 + 9) = 256(t^2 + 1) > 0$\uff0c<\/p>\n
\u5f26\u957f$|AB| = \\sqrt{1 + t^2} \\cdot \\frac{\\sqrt{\\Delta}}{4t^2 + 9} = \\frac{24(t^2 + 1)}{4t^2 + 9}$\uff0c<\/p>\n
\u540e\u7eed\u7ed3\u5408$|PM| = |PN|$\u63a8\u5bfc$t$\u7684\u5173\u7cfb\uff0c\u6700\u7ec8\u6c42\u5f97\u6700\u5c0f\u503c\u4e3a$4$\uff08\u8fc7\u7a0b\u7565\uff09\u3002<\/p>\n
\u56db\u3001\u6559\u5b66\u6ce8\u610f\u4e8b\u9879\uff08\u5bf9\u63a525\u7248\u8bfe\u6807\u4e0e\u6838\u5fc3\u7d20\u517b\uff09<\/p>\n
1. \u907f\u514d\u201c\u91cd\u516c\u5f0f\u8f7b\u7406\u89e3\u201d\uff1a\u786c\u89e3\u5b9a\u7406\u662f\u4ee3\u6570\u8fd0\u7b97\u7684\u201c\u7b80\u5316\u7248\u201d\uff0c\u9700\u5148\u8ba9\u5b66\u751f\u638c\u63e1\u5e38\u89c4\u8054\u7acb\u3001\u6d88\u5143\u3001\u97e6\u8fbe\u5b9a\u7406\u5e94\u7528\uff0c\u518d\u5f15\u5165\u516c\u5f0f\uff0c\u901a\u8fc7\u5bf9\u6bd4\u8fd0\u7b97\u8fc7\u7a0b\uff0c\u7406\u89e3\u516c\u5f0f\u7684\u5408\u7406\u6027\uff1b<\/p>\n
2. \u5206\u5c42\u6559\u5b66\u9002\u914d\uff1a
\n \u57fa\u7840\u5c42\uff1a\u638c\u63e1\u692d\u5706\u3001\u629b\u7269\u7ebf\u7684\u786c\u89e3\u516c\u5f0f\uff0c\u80fd\u89e3\u51b3\u76f4\u63a5\u6c42\u5f26\u957f\u3001\u4e2d\u70b9\u7684\u95ee\u9898\uff1b<\/p>\n
3. \u63d0\u9ad8\u5c42\uff1a\u7406\u89e3\u53cc\u66f2\u7ebf\u7684\u659c\u7387\u9650\u5236\u3001\u76f4\u7ebf\u8bbe\u7ebf\u6280\u5de7\uff08\u5982$x = ty + m$\u907f\u514d\u659c\u7387\u4e0d\u5b58\u5728\uff09\uff0c\u80fd\u7ed3\u5408\u5224\u522b\u5f0f\u6c42\u53c2\u6570\u8303\u56f4\uff1b<\/p>\n
4. \u62d4\u9ad8\u5c42\uff1a\u7ed3\u5408\u76f4\u89c2\u60f3\u8c61\u7d20\u517b\uff0c\u7528GeoGebra\u6f14\u793a\u76f4\u7ebf\u4e0e\u66f2\u7ebf\u7684\u4f4d\u7f6e\u5173\u7cfb\uff0c\u5206\u6790\u516c\u5f0f\u4e2d\u53c2\u6570\uff08$k$\u3001$m$\uff09\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd\uff1b<\/p>\n
5. \u9ad8\u8003\u9002\u914d\u63d0\u9192\uff1a\u786c\u89e3\u5b9a\u7406\u53ef\u7528\u4e8e\u8349\u7a3f\u7eb8\u5feb\u901f\u8ba1\u7b97\u6216\u9a8c\u8bc1\u7b54\u6848\uff0c\u4f46\u7b54\u9898\u5361\u9700\u5448\u73b0\u5173\u952e\u6b65\u9aa4\uff08\u5982\u8054\u7acb\u65b9\u7a0b\u3001\u5224\u522b\u5f0f\u3001\u97e6\u8fbe\u5b9a\u7406\uff09\uff0c\u907f\u514d\u4ec5\u5199\u516c\u5f0f\u5bfc\u81f4\u5931\u5206\uff1b<\/p>\n
6. \u6613\u9519\u70b9\u7a81\u7834\uff1a
\n \u53cc\u66f2\u7ebf\u7684$A = b^2 – a^2k^2$\uff0c\u9700\u6ce8\u610f$A \\neq 0$\uff08\u5426\u5219\u76f4\u7ebf\u4e0e\u6e10\u8fd1\u7ebf\u5e73\u884c\uff09\uff1b<\/p>\n
7. \u629b\u7269\u7ebf\u8bbe\u7ebf\u65f6\uff0c\u7126\u70b9\u5f26\u4f18\u5148\u7528$x = ty + \\frac{p}{2}$\uff0c\u51cf\u5c11\u659c\u7387\u4e0d\u5b58\u5728\u7684\u8ba8\u8bba\uff1b<\/p>\n
8. \u5f26\u957f\u516c\u5f0f\u4e2d$\\sqrt{1 + k^2}$\uff0c\u82e5\u76f4\u7ebf\u5782\u76f4$x$\u8f74\uff0c\u9700\u5355\u72ec\u8ba1\u7b97\uff08$k$\u4e0d\u5b58\u5728\uff0c\u5f26\u957f\u4e3a$|y_1 – y_2|$\uff09\u3002<\/p>\n
\u4e94\u3001\u603b\u7ed3<\/p>\n
\u5706\u9525\u66f2\u7ebf\u786c\u89e3\u5b9a\u7406\u662f\u9ad8\u4e2d\u6570\u5b66\u89e3\u6790\u51e0\u4f55\u7684\u201c\u9ad8\u6548\u5de5\u5177\u201d\uff0c\u6838\u5fc3\u4ef7\u503c\u5728\u4e8e\u7b80\u5316\u91cd\u590d\u8fd0\u7b97\uff0c\u8ba9\u5b66\u751f\u805a\u7126\u903b\u8f91\u63a8\u7406\u4e0e\u51e0\u4f55\u610f\u4e49\u5206\u6790\u3002\u6559\u5b66\u4e2d\u9700\u4ee5\u201c\u7406\u89e3\u63a8\u5bfc\u8fc7\u7a0b\u201d\u4e3a\u57fa\u7840\uff0c\u7ed3\u5408\u5206\u5c42\u6559\u5b66\u4e0e\u6280\u672f\u5de5\u5177\uff08GeoGebra\uff09\uff0c\u65e2\u5e2e\u52a9\u5b66\u751f\u5feb\u901f\u89e3\u9898\uff0c\u53c8\u57f9\u517b\u6570\u5b66\u8fd0\u7b97\u3001\u76f4\u89c2\u60f3\u8c61\u7b49\u6838\u5fc3\u7d20\u517b\uff0c\u9002\u914d25\u7248\u8bfe\u6807\u5bf9\u201c\u77e5\u8bc6\u5e94\u7528\u4e0e\u7d20\u517b\u843d\u5730\u201d\u7684\u8981\u6c42\u3002\u5efa\u8bae\u901a\u8fc7\u9ad8\u8003\u771f\u9898\u4e13\u9879\u8bad\u7ec3\uff0c\u8ba9\u5b66\u751f\u719f\u7ec3\u638c\u63e1\u516c\u5f0f\u7684\u9002\u7528\u573a\u666f\u4e0e\u6613\u9519\u70b9\uff0c\u63d0\u5347\u89e3\u6790\u51e0\u4f55\u5927\u9898\u7684\u5f97\u5206\u6548\u7387\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u5706\u9525\u66f2\u7ebf\u786c\u89e3\u5b9a\u7406\uff08\u9ad8\u6548\u89e3\u9898\u5de5\u5177…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-44","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/posts\/44","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/comments?post=44"}],"version-history":[{"count":1,"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/posts\/44\/revisions"}],"predecessor-version":[{"id":45,"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/posts\/44\/revisions\/45"}],"wp:attachment":[{"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/media?parent=44"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/categories?post=44"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.beitaiku.com\/index.php\/wp-json\/wp\/v2\/tags?post=44"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}