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高中数学中讲了三种二次曲线,椭圆、双曲线和抛物线.但是在平面直角坐标系下,考察一个二次代数方程Ax2+2Bxy+Cy2+Dx+Ey+F=0,判断它属于哪一类的二次曲线,以及它的对称轴、焦点坐标,长短轴(椭圆),实轴和虚轴(双曲线),准线(抛物线)的方程等,一般来说,并不直观和直接.本文就是对于一个一般的二次方程,通过分析,得出相应的结论.一、坐标问题
In high school mathematics, there are three types of conic, ellipse, hyperbola and parabola, but in the Cartesian coordinate system, consider a quadratic algebra equation Ax2 + 2Bxy + Cy2 + Dx + Ey + F = 0, A class of conics, as well as its symmetry axis, focal coordinates, long axis (ellipse), real axis and imaginary axis (hyperbola), quasi-line (parabola) equation, in general, is not intuitive and direct This article is for a general quadratic equation, through analysis, draw the corresponding conclusions.