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5. 一般柱面

5. 一般柱面. 定义：设空间中一条曲线 Γ 和方向 ν ，则过 Γ 上每一点与 ν 平行的直线 l 的集合构成的曲面叫柱面。这些直线叫柱面的母线， Γ 叫柱面的准线， ν 叫母线的方向。一般方程为： F(x,y,z)=0. 5.1 不含 z 的柱面 5.2 不含 x 的柱面. 5.1 一般 柱面之 F ( x,y ) = 0. z. ( x,y,z ). M. 母线. 0. y. F ( x,y ) = 0. z = 0. x. 准线. F ( x,y ) = 0 表示母线平行于 z 轴的柱面. ( 不含 z ).

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5. 一般柱面

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  1. 5.一般柱面 定义：设空间中一条曲线Γ和方向ν，则过Γ上每一点与ν平行的直线l的集合构成的曲面叫柱面。这些直线叫柱面的母线，Γ叫柱面的准线，ν叫母线的方向。一般方程为： F(x,y,z)=0. 5.1 不含z的柱面 5.2 不含x的柱面

  2. 5.1一般柱面之F(x,y)=0 z (x,y,z) M 母线 0 y F( x,y )=0 z= 0 x 准线 F(x,y)=0表示母线平行于z轴的柱面 (不含z) 曲面S上每一点都满足方程； S (x, y, 0) N 点N满足方程，故点M满足方程 返 回 曲面S外的每一点都不满足方程

  3. 5.2一般柱面之F(y, z)=0 F( y, z )=0 准线 z x = 0 母线 0 y x (不含x) F(y,z)=0表示母线平行于x轴的柱面 返 回

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