指出下列方程在空间直角坐标系下所表示的曲面:
(1)12x+2y+z=6;
(2)x2+z2=2z;
(3)z=2+x2+y2;
(4)x2+4y2=4y;
(5)z=2y2;
(6)x2+8y2+4z2=36;
(7)x2-4y2=4y;
(8)x2-4y2-z2=0.
(1)平面; (2)圆柱面; (3)旋转抛物面; (4)椭圆柱面; (5)抛物柱面; (6)椭球面; (7)双曲柱面; (8)椭圆锥面
指出下列方程在空间直角坐标系下所表示的曲面:
(1)12x+2y+z=6;
(2)x2+z2=2z;
(3)z=2+x2+y2;
(4)x2+4y2=4y;
(5)z=2y2;
(6)x2+8y2+4z2=36;
(7)x2-4y2=4y;
(8)x2-4y2-z2=0.
(1)平面; (2)圆柱面; (3)旋转抛物面; (4)椭圆柱面; (5)抛物柱面; (6)椭球面; (7)双曲柱面; (8)椭圆锥面