已知直线[tex=3.643x1.214]DomkRS3EUntZvlTFE20vzQ==[/tex]过[tex=2.286x1.357]IVQHL7gpVvGMeTU2JgKtIg==[/tex]点，当直线[tex=3.643x1.214]DomkRS3EUntZvlTFE20vzQ==[/tex]与抛物线[tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex]所围图形面积最小时，[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]，[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]应取何值？

2022-06-30

已知直线[tex=3.643x1.214]DomkRS3EUntZvlTFE20vzQ==[/tex]过[tex=2.286x1.357]IVQHL7gpVvGMeTU2JgKtIg==[/tex]点，当直线[tex=3.643x1.214]DomkRS3EUntZvlTFE20vzQ==[/tex]与抛物线[tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex]所围图形面积最小时，[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]，[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]应取何值？

答案：

由已知[tex=3.714x1.214]m8UOHkip+jLR5q8rpvdXTA==[/tex]( 即[tex=1.714x1.0]/VYz8Y4gTr+R9IrB4bHWCQ==[/tex]).设直线[tex=3.714x1.214]bt+i8pT1tTAdtOJOk5iScg==[/tex]与抛物线[tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex]两交点的横坐标为[tex=0.929x1.0]wVICVfwx/+W8A4DO0okxuw==[/tex]， [tex=0.929x1.0]ZqQiJnMrjfY80hciAkpyGg==[/tex][tex=4.0x1.357]dyWeKaSeAY6b1JXPRVw+rvdWOdpJEx12Pz90vYxWs2Y=[/tex]（如图），[img=253x172]1776bf3df76aab6.png[/img]则它所围面积[tex=10.143x2.786]DLp1yxd7iTQVT4I5o5+yyDTYK8l0mfLn5jz6Wp7zEf7nNKx1XYq4SOyf0Jqt1NvEKFRj1+jVsqLTxoi1B6aFng==[/tex]，即[tex=16.429x2.357]dJI68EbyEzwABRbhER00+xAOfSsZjU0gH6khzobDQGO6DzU2gulEQwrRAIUCFSMlJo1YU8BFlC+BOc+mT5LhtrWtflxphD87PvEfz/Ce8UvJ8tNjYDPCYFAzOcvA3eN62RDN1l8x9CiK557oyYxKreN4QlHRnozrXRSgLiF/4Iw=[/tex].又因为[tex=12.429x3.357]7EJHVCtO2IWq3KpdB+jQsgUIZfyJCBvqQLzx50APs25P0dzszPgg7FQWgT8rKS4VPbF3J0mSY41iowns4sZAisb33I2YT2ghRAxyl7g7q/JMcBQlDaKJtlIz5UfNrjbH[/tex].设[tex=0.929x1.0]csWE1emkPE6uH7oNfdpoVw==[/tex]，[tex=0.929x1.0]P1W9HQFke5bhAiy3bCsg0Q==[/tex]是此方程的两根，则有[tex=3.929x1.143]VDA3hcKeZBP5LIsZn6m4bw==[/tex]，[tex=3.929x1.214]40mzxDN0sOmOLXmYq+fabg==[/tex][tex=11.0x4.786]+JhuVKoefT40XeFGWkVX1XN+CJ5E4iEHkWdIG1uS9fvRaZRCkhhnte5fXIgnw2Eo/WonavgkwHbKWPheAkANjhdBqF/wOs0qETGfnNtN1EIP2RObGIjv6v7+sP1tf6qGFXKb4B/1bLHOMKx8XfXAAD9aTeOPwMrqTLKEAX/RDyC4pWjNwhdYp3mk+gyeENx8XEhr8fvot1CTFWTLpYZm2Q==[/tex]又[tex=11.714x3.214]Nzzcj2SCmhAiTZWyuC5r55KYSsPxccN0Nm4yvb8WscS7/3xtcbdmSmE1NHwMh6tczdPVi/Y3GzvBJVl5/rKvGsazP+Wfvlz/IcSH7d27iGgRmEJYf1eYE6mkEaGrGjtWCwMU/TJPJH0+fxjs+RU/5Q==[/tex][tex=14.786x4.0]LsqalcgrkiKmI0NO66zGJ8BYOoY8u11kmZyxC+TUdMcAYE0AnkFFT8ojkGEOMsP86G+HiHiMiltQGPYKJyVhBMvNK5jQfXxcubCzhnXxSNwC8XazwrjWZQoqC0P5OjxfXvdVzGGVdHetNx0iWFwj8p1Kc7/qWjrpVNHe/TOIYEkZCWbKeQECH7gqRHubZkbt[/tex]故[tex=19.214x4.286]cAZqvGRIG2T/e++7G0q8NKp2R7ouSUkvskeN0ckG5ji0I+agzhiO6zQM1L7KCyj2Eyfa5kVx/UVcI9veJeCjVf21NIin4drSF2yKRMsdYaRijUGFEyGbKH2BCoI67O/l7UUEZNA/MFsE/mnsmGdNUYCb3vAHqO6H8JBG0cphOmCJXjHEPueEOZNVPpmCpmBB[/tex]令[tex=9.214x2.429]eHmJ6WkcVxLNZ4Gfz3qUft+Ds1i53UYumhUWrpL9ahnAG3AzokAyUjVzlD3xwf8mvTwEJ4A1mJMsYQXN48QBv0rXbk/Vd/cwioadAtyO/w4=[/tex]，则[tex=1.857x1.0]6kXYmlOKKE+OTRD+ArKMxg==[/tex]，故当[tex=2.429x1.0]32G4y8Y6/zeJvS1a7IxuJw==[/tex]时，[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]有最小值48，故[tex=2.429x1.0]32G4y8Y6/zeJvS1a7IxuJw==[/tex]，b=1.

举一反三

内容

0
计算下述[tex=1.143x1.0]oTcZ8bPOd5+p8E1UHN7wXA==[/tex]阶行列式（主对角线上元素都是[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]，反对角线上元素都是[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]，空缺处的元素为0）：[tex=14.357x7.214]BafYOyQLkfv749f2fydiSmuFaORJrmT8ZJIXGdw44f1aEpC52UG/9KaK/rVnUNciUh3QoBqaPPxfmlIg/phge+h4iq0ABGDReZk1AL0sZKzKnThLESNQm78N48nK4v5O+GmV/flx/lbKKFGOzBOQhYxNt+leiRpulVjqMeOFBfnI0RXZdSR7MVvsUvgTHcf+ugGSltGkhpnoxUoJeFlxsZdoHZzCrpQrZ4mwb1kz/X/Fqe167F6aEL+T1v5e+y8WvVKhcL8g9UtTTbtwM8lNug==[/tex]
1
自变量 [tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex] 取何值时,抛物线 [tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex] 与 [tex=2.786x1.429]GAL3wqj4JSMLlcvcfbE2gA==[/tex] 的切线平行.
2
求由抛物线[tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex]和[tex=3.571x1.429]x2ulPC9h41k0fVEnCwicBQ==[/tex]所围图形的面积.
3
抛物线[tex=3.571x1.429]FsdbO/anc2tEhhllnrp/TA==[/tex]与直线[tex=3.643x1.214]yXDSWbgQk9xG6JHAY6biNQ==[/tex]相交于[tex=0.786x1.0]kEam2pLJe4uAYVdcny2W5g==[/tex]，[tex=0.786x1.0]EsJDtGYVBcAkNM+hi9jDJg==[/tex]两点，[tex=0.714x1.0]J/aA9EEo0KmJFnWWfX7LmQ==[/tex]为抛物线上且在直线[tex=3.643x1.214]N8T1ZQBfxAJssmYz9OYAsw==[/tex]上方的任一点，求[tex=3.143x1.214]BypMH6cWAb0x8gikbHmOkm8G6z9CQ+Rgr92Svssi5/0=[/tex]面积的最大值.
4
求向量[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]与[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的夹角：[tex=5.429x1.357]28vNNArDuRRnb+06piGt7g==[/tex]，[tex=6.143x1.357]Uqwu1QGYB2waFjV52ImPKg==[/tex] .