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];
解：由方程得：[tex=6.429x2.929]fnpmC2J6JmQBLyo5NmGAz3XnUUxHUeIq3DGy5vQhT+qFyHRu2nVpPviFWRGBrmg1bI+xO+SrDlNHdzUsnnv/neVRAy+7BrNQbzvr6ocgeYI=[/tex],消去 c 有:[tex=3.214x2.429]dXga0r4SJTh9I2AwV7inFrHi64idONELN1oe4UlvF3g=[/tex],则所求等角轨线的微分方程为[tex=7.357x3.071]dXga0r4SJTh9I2AwV7inFrCkn3LtrtGdTAIBEp2L043aTgHFbU2xmCKpM8xijI6gPrH69z+yoEg57yZLVkiQbNpKC5AbhS0GmIWFkBjtsw4EEti85WEQQA/l/yLGFwviXZRBLFxJhgr1ujy0OBkLQQ==[/tex],亦即[tex=4.714x1.214]23aODHYVp+GnABSo3pOL0g==[/tex],所以所求等角轨线族为[tex=3.571x1.214]n978BchEx2qDc84ssxSOLQ==[/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=2.286x1.0]sdiORd21alyeXynfkZsstw==[/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).
- 求下列各曲线族的正交轨线族：[tex=3.214x1.429]52BNqejfXy656ai6MPZ1HQ==[/tex];
内容
- 0
求下列各曲线族的正交轨线族：[tex=3.857x1.429]VjKK0zi64WcnKcnoL9RcPQ==[/tex]
- 1
求下列各曲线族的正交轨线族：[tex=2.286x1.0]sdiORd21alyeXynfkZsstw==[/tex];
- 2
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}
- 3
求下列各曲线族的正交轨线族：[tex=4.786x1.429]rQ0cSvXcV9twzEOC6TY0TFJFP/Wb8q7FsywHOTDjoyQ=[/tex];
- 4
已知曲线的切线和切点的矢径相交成定角[tex=0.571x0.786]HXNXn3AXpwdIpZt8+6oCEw==[/tex],求此曲线