{"id":365,"date":"2025-03-27T23:12:24","date_gmt":"2025-03-27T15:12:24","guid":{"rendered":"https:\/\/tilearn.space\/?p=365"},"modified":"2025-03-27T23:37:22","modified_gmt":"2025-03-27T15:37:22","slug":"2024%e5%b1%8a%e5%ae%9d%e5%b1%b1%e5%8c%ba%e5%88%9d%e4%b8%89%e4%ba%8c%e6%a8%a1%e6%95%b0%e5%ad%a6%e8%af%95%e5%8d%b7%e7%b2%be%e8%ae%b2%ef%bc%88%e7%ac%ac24%e9%a2%98%ef%bc%89","status":"publish","type":"post","link":"https:\/\/tilearn.space\/?p=365","title":{"rendered":"2024\u5c4a\u5b9d\u5c71\u533a\u521d\u4e09\u4e8c\u6a21\u6570\u5b66\u8bd5\u5377\u7cbe\u8bb2\uff08\u7b2c24\u9898\uff09"},"content":{"rendered":"
\n

\u9898\u76ee\uff1a<\/h3>\n

24. \u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfbxOy\u4e2d\uff08\u5982\u56fe\uff09\uff0c\u5df2\u77e5\u5f00\u53e3\u5411\u4e0b\u7684\u629b\u7269\u7ebf\\(y = ax^2 – 2x + 4\\)\u7ecf\u8fc7\u70b9\\(P(0, 4)\\)\uff0c\u9876\u70b9\u4e3a\\(A\\)\u3002<\/p>\n

\"4ec48c249b8da930380d14294a94c0cc\"<\/p>\n

    \n
  1. \u6c42\u76f4\u7ebf\\(PA\\)\u7684\u8868\u8fbe\u5f0f\u3002<\/li>\n
  2. \u5982\u679c\u5c06\\(\\triangle POA\\)\u7ed5\u70b9\\(O\\)\u9006\u65f6\u9488\u65cb\u8f6c90\u00b0\uff0c\u70b9\\(A\\)\u843d\u5728\u629b\u7269\u7ebf\u4e0a\u7684\u70b9\\(Q\\)\u5904\uff0c\u6c42\u629b\u7269\u7ebf\u7684\u8868\u8fbe\u5f0f\u3002<\/li>\n
  3. \u5c06(2)\u4e2d\u5f97\u5230\u7684\u629b\u7269\u7ebf\u6cbf\u5c04\u7ebf\\(PA\\)\u5e73\u79fb\uff0c\u5e73\u79fb\u540e\u629b\u7269\u7ebf\u7684\u9876\u70b9\u4e3a\\(B\\)\uff0c\u4e0ey\u8f74\u4ea4\u4e8e\u70b9\\(C\\)\u3002\u5982\u679c\\(PC = \\sqrt{2}AB\\)\uff0c\u6c42\\(\\tan \\angle PBC\\)\u7684\u503c\u3002<\/li>\n<\/ol>\n

    \u8be6\u7ec6\u89e3\u7b54\uff1a<\/h3>\n

    (1) \u7531\\(y = ax^2 – 2x + 4 = a(x – \\frac{1}{a})^2 + 4 – \\frac{1}{a}\\)\uff0c\u53ef\u5f97\\(A(\\frac{1}{a}, 4 – \\frac{1}{a})\\)\u3002<\/p>\n

    \u7531\u9898\u610f\u8bbe\u76f4\u7ebf\\(PA\\)\u7684\u8868\u8fbe\u5f0f\u4e3a\\(y = kx + 4(k \\neq 0)\\)\u3002<\/p>\n

    \u5c06\\(A(\\frac{1}{a}, 4 – \\frac{1}{a})\\)\u4ee3\u5165\u5f97\uff1a\\(\\frac{k}{a} + 4 = 4 – \\frac{1}{a}\\)\uff0c\u89e3\u5f97\\(k = -1\\)\u3002<\/p>\n

    \u6240\u4ee5\uff0c\u76f4\u7ebf\\(PA\\)\u7684\u8868\u8fbe\u5f0f\u4e3a\\(y = -x + 4\\)\u3002<\/p>\n

    (2) \u7531\u629b\u7269\u7ebf\u5f00\u53e3\u5411\u4e0b\u4e14\u8fc7\u70b9\\(P(0, 4)\\)\uff0c\\(\\triangle POA\\)\u7ed5\u70b9\\(O\\)\u9006\u65f6\u9488\u65cb\u8f6c90\u00b0\uff0c\u70b9\\(A\\)\u7684\u5bf9\u5e94\u70b9\\(Q\\)\u5728\u629b\u7269\u7ebf\u4e0a\u3002<\/p>\n

    \"\"<\/p>\n

    \u8fc7\u70b9\\(A\\)\u3001\\(Q\\)\u5206\u522b\u4f5c\\(AM \\perp y\\)\u8f74\uff0c\\(QN \\perp y\\)\u8f74\uff0c\u5782\u8db3\u5206\u522b\u4e3a\u70b9\\(M\\)\u3001\\(N\\)\u3002<\/p>\n

    \u4e8e\u662f\\(\\triangle OAM \\cong \\triangle QON\\)\uff0c\u5219\u7531\\(A(\\frac{1}{a}, 4 – \\frac{1}{a})\\)\u5f97\\(Q(-\\frac{1}{a}, 4 – \\frac{1}{a})\\)\u3002<\/p>\n

    \u4ee3\u5165\\(y = ax^2 – 2x + 4\\)\u5f97\\(8a^2 + 2a – 1 = 0\\)\u3002<\/p>\n

    \u89e3\u5f97\\(a = -\\frac{1}{2}\\)\u6216\\(a = \\frac{1}{4}\\)\uff08\u820d\u53bb\uff09\u3002<\/p>\n

    \u6240\u4ee5\uff0c\\(a\\)\u7684\u503c\u4e3a\\(\\frac{1}{2}\\)\u3002<\/p>\n

    (3) \u7531(2)\u5f97\\(y = \\frac{1}{2}x^2 – 2x + 4 = \\frac{1}{2}(x + 2)^2 + 6\\)\uff0c\\(A(-2, 6)\\)\u3002<\/p>\n

    \u8bbe\u5e73\u79fb\u540e\u7684\u629b\u7269\u7ebf\u8868\u8fbe\u5f0f\u4e3a\\(y = \\frac{1}{2}(x – m)^2 + 4 – m\\)\u3002<\/p>\n

    \"df8e2aac7221f9552acda0e55eb8bba2\"<\/p>\n

    \u5219\\(B(m, 4 – m)\\)\uff0c\\(C(0, \\frac{1}{2}m^2 – m + 4)\\)\u3002<\/p>\n

    \u70b9\\(B\\)\u5728\u70b9\\(A\\)\u7684\u4e0a\u65b9\uff0c\u70b9\\(C\\)\u5728\u70b9\\(P\\)\u7684\u4e0b\u65b9\u3002<\/p>\n

    \u4e8e\u662f\uff0c\\(AB = \\sqrt{(m + 2)^2 + (m + 2)^2} = \\sqrt{2}|m + 2|\\)\u3002<\/p>\n

    \\(PC = 4 – (\\frac{1}{2}m^2 – m + 4) = \\frac{1}{2}m^2 – m\\)\u3002<\/p>\n

    \u7531\\(PC = \\sqrt{2}AB\\)\uff0c\u53ef\u5f97\\(\\frac{1}{2}m^2 – m = -2(m + 2)\\)\u3002<\/p>\n

    \u89e3\u5f97\\(m = -4\\)\u6216\\(m = -2\\)\uff08\u820d\u53bb\uff09\u3002<\/p>\n

    \u4e8e\u662f\\(B(-4, 8)\\)\uff0c\\(C(0, 0)\\)\u3002<\/p>\n

    \u5728\\(\\triangle CDP\\)\u4e2d\uff0c\\(\\angle DPC = 45^\\circ\\)\uff0c\\(PC = 4\\)\uff0c\u53ef\u5f97\\(CD = DP = 2\\sqrt{2}\\)\u3002<\/p>\n

    \\(BP = \\sqrt{(0 + 4)^2 + (8 – 4)^2} = 4\\sqrt{2}\\)\uff0c\u4e8e\u662f\\(BD = DP + BP = 6\\sqrt{2}\\)\u3002<\/p>\n

    \u6240\u4ee5\uff0c\u5728\\(\\triangle CDB\\)\u4e2d\uff0c\\(\\tan \\angle PBC = \\frac{CD}{BD} = \\frac{2\\sqrt{2}}{6\\sqrt{2}} = \\frac{1}{3}\\)\u3002<\/p>\n

    \u76f8\u5173\u77e5\u8bc6\u70b9\u590d\u4e60\uff1a<\/h3>\n

    1. \u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\u53ca\u5176\u6027\u8d28\u3002<\/p>\n

    2. \u76f4\u7ebf\u7684\u659c\u7387\u548c\u65b9\u7a0b\u3002<\/p>\n

    3. \u5e73\u9762\u51e0\u4f55\u4e2d\u7684\u65cb\u8f6c\u548c\u5e73\u79fb\u53d8\u6362\u3002<\/p>\n

    \u6613\u9519\u63d0\u793a\u548c\u62d3\u5c55\uff1a<\/h3>\n

    1. \u6ce8\u610f\u629b\u7269\u7ebf\u7684\u5f00\u53e3\u65b9\u5411\u548c\u9876\u70b9\u5750\u6807\u7684\u5173\u7cfb\u3002<\/p>\n

    2. \u5728\u8fdb\u884c\u51e0\u4f55\u53d8\u6362\u65f6\uff0c\u6ce8\u610f\u70b9\u7684\u5750\u6807\u53d8\u5316\u89c4\u5f8b\u3002<\/p>\n

    3. \u89e3\u9898\u8fc7\u7a0b\u4e2d\u8981\u6ce8\u610f\u4ee3\u6570\u8fd0\u7b97\u7684\u51c6\u786e\u6027\u3002<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    \u9898\u76ee\uff1a 24. \u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfbxOy\u4e2d\uff08\u5982\u56fe\uff09\uff0c\u5df2\u77e5\u5f00\u53e3\u5411\u4e0b\u7684\u629b\u7269\u7ebf\\(y = ax^2 – 2 […]<\/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-365","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/365","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=365"}],"version-history":[{"count":4,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/365\/revisions"}],"predecessor-version":[{"id":372,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/365\/revisions\/372"}],"wp:attachment":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=365"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=365"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=365"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}