每日一道選填題3（圓錐曲線）

2022-09-05 17:55 作者:因戀相思久 0人讀過 | 我要投稿

5.已知拋物線 $x%5E2%3D32y%20$ 的焦點(diǎn) $%E4%B8%BAF%EF%BC%8C%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8A%E4%B8%80%E7%82%B9A%E6%BB%A1%E8%B6%B3%5Cvert%20AF%20%5Cvert%20%3D10$ ，則直線 $AF$ 的斜率為（）

$a.-%5Cfrac%7B3%7D%7B4%7D%20$

$b.%5Cfrac%7B3%7D%7B4%7D%20$

$c.%5Cpm%20%5Cfrac%7B3%7D%7B4%7D%20$

$d.%5Cpm%20%5Csqrt%7B2%7D%20$

$%E6%98%BE%E7%84%B6P%3D16%EF%BC%8CF%EF%BC%880%2C8%EF%BC%89$

$%E6%A0%B9%E6%8D%AE%E6%8A%9B%E7%89%A9%E7%BA%BF%E5%AE%9A%E4%B9%89$

$8%2By_%7BA%7D%20%3D10$

$%E5%8D%B3y_%7BA%7D%20%3D2%EF%BC%8Cx_%7BA%7D%20%3D%5Cpm%208$

$%E6%89%80%E4%BB%A5k%3D%5Cfrac%7B2-8%7D%7B0%5Cpm8%20%7D%20%3D%5Cpm%20%5Cfrac%7B3%7D%7B4%7D%20%EF%BC%8C%E9%80%89c$

技巧點(diǎn)：

$%E6%8A%9B%E7%89%A9%E7%BA%BF%E5%AE%9A%E4%B9%89$

$16.%E5%B7%B2%E7%9F%A5%E7%82%B9F%E4%B8%BA%E5%8F%8C%E6%9B%B2%E7%BA%BFC%EF%BC%9A%5Cfrac%7Bx%5E2%20%7D%7Ba%5E2%20%7D-%20%5Cfrac%7By%5E2%20%7D%7Bb%5E2%20%7D%20%3D1%EF%BC%88a%EF%BC%8Cb%EF%BC%9E0%EF%BC%89$ 的左焦點(diǎn)，過點(diǎn) $F$ 且斜率為1的直 $%E7%BA%BF%E4%BA%A4C%E4%BA%8EA%EF%BC%8CB%E4%B8%A4%E7%82%B9%EF%BC%8C%E8%8B%A5%5Cvec%7BAF%7D%20%3D3%5Cvec%7BBF%7D%20$ ，則 $C$ 的離心率為 $%5Cast%20%5Cast%20%5Cast%20$

$tan%5Ctheta%20%3D1%5CRightarrow%20%5Ctheta%20%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20$

$%E4%B8%94F%EF%BC%8CA%EF%BC%8CB%E5%85%B1%E7%BA%BF$

$%E6%89%80%E4%BB%A5%5Cvert%20AF%20%5Cvert%20%3D3%5Cvert%20BF%20%5Cvert%20$

$%E5%BD%93A%EF%BC%8CB%E5%9C%A8%E5%90%8C%E4%B8%80%E6%94%AF%E4%B8%8A%E6%97%B6$

$%E5%9B%A0%E4%B8%BA%5Cvert%20BF%20%5Cvert%20%3D%5Cfrac%7Bb%5E2%20%7D%7Ba%2Bccos%5Ctheta%20%7D%20$

$%5Cvert%20AF%20%5Cvert%20%3D%5Cfrac%7Bb%5E2%20%7D%7Ba-ccos%5Ctheta%20%7D%20$

$%E6%89%80%E4%BB%A5%5Cfrac%7Bb%5E2%20%7D%7Ba-ccos%5Ctheta%20%7D%20%20%3D%5Cfrac%7B3b%5E2%20%7D%7Ba%2Bccos%5Ctheta%20%7D%20$

$%E8%A7%A3%E5%BE%97e%3D%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D%20%EF%BC%88%E8%88%8D%EF%BC%89$

$%E5%BD%93A%EF%BC%8CB%E5%BC%82%E4%BA%8E%E4%B8%80%E6%94%AF%E6%97%B6$

$%5Cvert%20BF%20%5Cvert%20%3D%5Cfrac%7Bb%5E2%20%7D%7Ba%2Bccos%5Ctheta%20%7D%20$

$%5Cvert%20AF%20%5Cvert%20%3D%5Cfrac%7Bb%5E2%20%7D%7Bccos%5Ctheta%20-a%7D%20$

$%E6%89%80%E4%BB%A5%5Cfrac%7Bb%5E2%20%7D%7Bccos%5Ctheta-a%20%7D%20%20%3D%5Cfrac%7B3b%5E2%20%7D%7Ba%2Bccos%5Ctheta%20%7D%20$

$%E8%A7%A3%E5%BE%97e%3D2%5Csqrt%7B2%7D%20$

技巧點(diǎn)：

$%E5%8F%8C%E6%9B%B2%E7%BA%BF%E7%9A%84%E5%B7%A6%E7%84%A6%E7%82%B9%E4%B8%BAF%EF%BC%8CAB%E4%B8%BA%E7%84%A6%E7%82%B9%E5%BC%A6%EF%BC%8C%5Ctheta%20%E4%B8%BA%E5%80%BE%E6%96%9C%E8%A7%92$

$%E5%90%8C%E6%94%AFe%5Cvert%20cos%5Ctheta%20%20%5Cvert%20%3D%5Cvert%20%5Cfrac%7B%5Clambda%20-1%7D%7B%5Clambda%2B1%20%7D%20%20%5Cvert%20%EF%BC%88%5Clambda%20%E4%B8%BA%E7%84%A6%E5%8D%8A%E5%BE%84%E4%B9%8B%E6%AF%94%EF%BC%89$

$%E5%BC%82%E6%94%AFe%5Cvert%20cos%5Ctheta%20%20%5Cvert%20%3D%5Cvert%20%5Cfrac%7B%5Clambda%20%2B1%7D%7B%5Clambda-1%20%7D%20%20%5Cvert%20%EF%BC%88%5Clambda%20%E4%B8%BA%E7%84%A6%E5%8D%8A%E5%BE%84%E4%B9%8B%E6%AF%94%EF%BC%89$

$%E5%90%8C%E6%94%AF%5Cvert%20BF%20%5Cvert%20%3D%5Cfrac%7Bb%5E2%20%7D%7Ba%2Bccos%5Ctheta%20%7D%20%EF%BC%8C%5Cvert%20AF%20%5Cvert%20%3D%5Cfrac%7Bb%5E2%20%7D%7Ba-ccos%5Ctheta%20%7D%20$

$%E5%BC%82%E6%94%AF%5Cvert%20BF%20%5Cvert%20%3D%5Cfrac%7Bb%5E2%20%7D%7Ba%2Bccos%5Ctheta%20%7D%20%EF%BC%8C%5Cvert%20AF%20%5Cvert%20%3D%5Cfrac%7Bb%5E2%20%7D%7B-a%2Bccos%5Ctheta%20%7D%20$