试求满足顶点在[tex=4.143x1.357]UlCROSqACEiUFW4htMlZVA==[/tex], 并与球面 [tex=5.643x1.429]JfMnpkdfUBckNje06oWbk/BDZAzHaBBEbyZO6OqX4As=[/tex]外切于一圆的锥面方程.

2022-07-23

试求满足顶点在[tex=4.143x1.357]UlCROSqACEiUFW4htMlZVA==[/tex], 并与球面 [tex=5.643x1.429]JfMnpkdfUBckNje06oWbk/BDZAzHaBBEbyZO6OqX4As=[/tex]外切于一圆的锥面方程.

答案：

[b]解法一 [/b]由题意知，所求雉面为圆雉面[tex=0.643x1.0]jLbabU9pW65GUKemsNBJWw==[/tex]，其轴线方程为[tex=13.857x2.143]UfGFIGzrTwhM5lHXty/B7altgnrKDeDePKdL8SboWk2sIbK9gWXPuBKuiSpvDkCEaWV5nU6Mjjr/eSXG9eefyRHULc9kongVrNvp7qEWDUg=[/tex]半顶角[tex=0.786x1.214]qA0Vzgx2NM7zOD6Jz+SWpg==[/tex]满足[tex=4.0x2.357]ygfZlvzwlafYYdOD9WDuZxlIS93bHrkCSsTi8W69B/Y=[/tex]于是[tex=6.286x1.357]z0cqVdUieKqTwhlPrl0Jy5ucmO1qq2D6Xg/bO8XgpTE=[/tex] 有[tex=12.214x3.857]IX8PRRcYNGk07lQaIIdqODiv9un4AbNuK7sSlvyItx5yBhlN+OVeK1Jijo02boBQnSZSpzrT/TQiTn7sIVjpt0J60ttRViKBz60DwxeoVOCobVBuZEawsxgfv069mM7Rn/ppTq8Aet5DCdBGqXMN3ilO1kKsdjrGb92fPc6VFqo=[/tex]亦即[tex=12.571x3.071]kD3LhzKfc+salT1NtDl3Hgoymta2Jh6RZFa6JBgnYL7bbYUagqGF0K0V0u9oeVsQu9vat3ZmhdLocFelt77FQ6U+rzpbdGBd94+Su/V3iSk=[/tex]解得[tex=16.143x1.429]Vw6Pwj/+M666vb+eOd1/5LmGIiDHks3cWyE/5qUa1IXKaQb1XsWZeFc/6B5bS8t85wRgUUUT86A+aPO80UiJfw==[/tex][b]解法二 [/b]由题意知，外切圆为 $x=k$ 与球面的交线，即[tex=10.286x2.929]ylZtzo8HXQ8y2xnJoH076sNdIDkBSnMDrsyz43JgpZEhi7hJ5K1b4gflDWWM+ffhzonvclpdIHAJQPcxIM7IAFGx/HrjbQj7U87C2c6HsdAxB39hNYXB7RIg0q0PTkLc[/tex]于是[tex=3.071x2.429]BkCcINahobdSKndkQyOkNo4G59kPBoYkSsuAX1Qj/1g=[/tex]从而 [tex=2.714x2.357]7o/HaRxWn1W7Qmub9H2ZCXnzouGb1zdkgQtRHjv9Wzw=[/tex]于是[tex=10.429x4.214]ylZtzo8HXQ8y2xnJoH076sNdIDkBSnMDrsyz43JgpZEhi7hJ5K1b4gflDWWM+ffh4iEDqOoRBoUnAd24PNr06CJUegC5I8FRL8syZBDxe0siMffVHpAvV8d1F3mOmMnC[/tex]为所求雉面 [tex=0.643x1.0]jLbabU9pW65GUKemsNBJWw==[/tex]的一条准线.设 [tex=5.786x1.357]jJaNDagHB00aCFtgCc+zxE4pUbY22Ic2WogCwbyBmXd7jrm27efpCEip/r2Fsal8[/tex] 为准线[tex=0.643x1.0]u7XUci3hWIE/S+TBToDPxA==[/tex]上任一点，[tex=1.357x1.214]QcSZflolD/TZzu4WluEs9g==[/tex]的母线方程为[tex=11.143x2.571]Gq6Ttazm+KH7A+8ODwsUkoZmGh/e6ZbQ7DMWrYyOQrf6X02JewLgyGLI+SRshMNJ6vsTsPXCdB2l879bgTpqayK8bPkwADZdQ0qE6HSyjSE=[/tex][tex=2.571x1.357]0M4nDkYYZoFTWvhWUzgVtQ==[/tex]且[tex=10.429x4.214]ylZtzo8HXQ8y2xnJoH076sNdIDkBSnMDrsyz43JgpZG1CjCEu+haRJymF8T/mNu6SDytHYGGieP7qBHgSrrrWNrBvUwfROHmvFzv9RcIMhazio5ouh5llGGynz2VHiX8xVTlr3VNHYfLmQTn9sIKGA==[/tex][tex=2.571x1.357]jW47KI4Gpyk2b0kdV7pU/g==[/tex]从式 [tex=2.571x1.357]AM6aUvjjkKxaIw8tQfbv2g==[/tex], 式[tex=2.571x1.357]aPCNyn7pAk7aFouOerO4zQ==[/tex] 中消去 [tex=3.5x1.0]ZQKQGr7S8GJiAdJeXaZNsYWrjflGnTVojVF45O+VmTk=[/tex]得[tex=15.571x1.429]2aIjZV2w4Z8sAl+NlncSeUQ5vzj8ERehxF8TVGGU/KmPHvLdFZN8qF/ZPxC3dZ8Y[/tex]

举一反三

内容

0
试求顶点是 [tex=4.214x1.357]5S9IkrA+8RhqnV2fE9efVA==[/tex]轴与平面[tex=6.786x1.214]aUOBDeMMO/d8zlqLFygkahOIs8jconLlt5A31o8k/Dc=[/tex] 垂直，并经过点[tex=4.143x1.357]AUTbze9rPnm7i75ELTVa0Q==[/tex] 的圆雉面的方程.
1
试求顶点在原点且包含 3 个坐标轴的圆锥面 [tex=0.643x1.0]jLbabU9pW65GUKemsNBJWw==[/tex] 的方程.
2
求锥面方程：顶点为[tex=4.786x1.357]N4eONjwLv40elECSNDzRYQ==[/tex]，准线为[tex=7.786x2.929]7EJHVCtO2IWq3KpdB+jQsv6FwiTm8kMJkqqPTKC4ZLDJjzXg12AtzoKuWn+xDIQB5YMPcKWrVEbSE9UoniO2+vt6Hj47LCgWpmopzKwqZPo=[/tex].
3
计算曲线积分 [tex=4.143x2.643]MMSpH2purKaqp8yxm15LtD2SzMHUaPWCnHbNLQ40Jrs=[/tex] 其中 [tex=0.714x1.0]YiLkHgl7MlxE+QjUplQUKA==[/tex] 是 [tex=5.643x1.429]JfMnpkdfUBckNje06oWbk/BDZAzHaBBEbyZO6OqX4As=[/tex] 与 [tex=1.786x1.0]hWEwca4gPBNKIXxqcnmuqg==[/tex] 的相交曲线,其方向为沿曲线依次经过 [tex=3.357x1.214]qjXBRp1sKhhK63ODl4Qfew==[/tex] 卦限.
4
求锥面方程：顶点为[tex=3.929x1.357]DTt9ETNlpjtJrTjgn1dyeg==[/tex]，准线为[tex=8.857x3.357]fnpmC2J6JmQBLyo5NmGAz89fzajrsY2GMIIvBoKtXjPe0rDBeeBBJJdDZkRFxPRIKyzlYe5x/fafOyYkOhuyHg4oCOoWYrhM7RDZBWTDlF8FCELReiJEF1pBNrAsocv1[/tex]。