求与下列各曲线相交成[tex=1.429x1.071]6wFjUg4eHIq46eioq8Pjcg==[/tex] 角的曲线族：[tex=2.286x1.0]sdiORd21alyeXynfkZsstw==[/tex];
解：由方程得：[tex=7.0x2.786]fnpmC2J6JmQBLyo5NmGAz951RknQ0y6iYD8CGTD0hT8O5N69Bx5cK6cC/fLl/bZoDnzlx6jWvmJblhhuORAggSgNYwvmqnwv/JMmjp1doyM=[/tex],消去 c 有:[tex=4.0x2.429]dXga0r4SJTh9I2AwV7inFvj2C/85B+y5L9ApPHXOOJY=[/tex]则所求等角轨线的微分方程为[tex=9.286x3.071]dXga0r4SJTh9I2AwV7inFiCrdQsL6MFCIIYrbrJ0RRvlFNLyb7GhF4hk5lR6PdrZ/FWMotMPM+v1iJCt4UIpa1nlA38ZR67irwigl7d8kUFDm2RNcGbPycbLyjoy1YPOi66I3dYdH5nQkZJG4SLXeC0zB5/uZdIx4OC1y2NKGjk=[/tex]亦即[tex=9.429x1.357]z0vjNCE9/KHHDVSlzjaONjOv/YkiAKK4ix4+AJRi610=[/tex]， 所以所求等角轨线族为[tex=6.214x1.429]g8Srs89pyAlORMfP1OSVw3fsAm/Ozpbn1d/QCDtpn3A=[/tex].
举一反三
- 求与下列各曲线相交成[tex=1.429x1.071]6wFjUg4eHIq46eioq8Pjcg==[/tex]角的曲线族：[tex=3.571x1.214]XfOKKLM16fBITKQCAN6kXg==[/tex];
- 求与下列各曲线相交成[tex=1.429x1.071]6wFjUg4eHIq46eioq8Pjcg==[/tex]角的曲线族：[tex=4.143x1.214]zS6dkWIziPDQVF1Jstha/A==[/tex];
- 求与下列各曲线相交成 [tex=1.429x1.071]6wFjUg4eHIq46eioq8Pjcg==[/tex]角的曲线族：[tex=3.857x1.286]6Ukrpt8KK27902/BhoLIpmLwtm+vNoiqBYa9ya2PeAY=[/tex];
- 求下列各曲线族的正交轨线族：[tex=2.286x1.0]sdiORd21alyeXynfkZsstw==[/tex];
- 求双曲线族 [tex=2.286x1.0]AyodH42rbSI7VONR6ZxvPA==[/tex] 的正交曲线
内容
- 0
求立方抛物线族 [tex=2.786x1.429]U7awraJpZqyDO/PMfhYIYQ==[/tex] 的正交轨线(即求一曲线族,这族曲线中的每一曲线与 [tex=2.786x1.429]U7awraJpZqyDO/PMfhYIYQ==[/tex]中每一条相交成直角).
- 1
求下列各曲线族的正交轨线族：[tex=3.214x1.429]52BNqejfXy656ai6MPZ1HQ==[/tex];
- 2
求下列各曲线族的正交轨线族：[tex=3.857x1.429]VjKK0zi64WcnKcnoL9RcPQ==[/tex]
- 3
平刺是指针刺与皮肤所成的角度为( ) 未知类型：{'options': ['[tex=1.929x1.071]EQVn6xTTVMeHKRmyIA8ktg==[/tex]', '[tex=1.429x1.071]HrADEgZoqo90D/eowIUddQ==[/tex]', '[tex=1.429x1.071]6wFjUg4eHIq46eioq8Pjcg==[/tex]', '[tex=1.429x1.071]Rgqj8bHi4xyxE+qK+DyGug==[/tex]', '[tex=1.429x1.071]3taJkn2+7hmo0Oj13QzJbQ==[/tex]'], 'type': 102}
- 4
求下列各曲线族的正交轨线族：[tex=4.786x1.429]rQ0cSvXcV9twzEOC6TY0TFJFP/Wb8q7FsywHOTDjoyQ=[/tex];