圆锥曲线新解

New Solution for Conic Curve

利用空间解析几何的方法求出旋转轴与z轴成一定角度的圆锥面方程,然后通过联立此圆锥面的方程与xOy面的方程z=0,得到不同的截线:当旋转轴与x轴的夹角大于半顶角时,截线是椭圆;当旋转轴与x轴的夹角小于半顶角时,截线是双曲线;当旋转轴与x轴的夹角等于半顶角时,截线是抛物线.

We use the method of analytic geometry to obtain the equation of the circular conical surface whose axis of rotation is at an angle to the z-axis. By solving this equation together with the equation for plane, we obtain different kinds of transversals, which are ellipse when the angle between the axis of rotation and the x-axis is larger than the semi-vertical angle of the conical surface, hyperbola when smaller, or parabola when equal.