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在解析几何中,我们常常利用曲线束解题,如过两相交直线交点的直线束,过两圆相交的交点的圆束,等等,其最大的作用是简化运算.下面谈谈二次曲线束在解几方面的应用.一、知识梳理二次曲线方程ax~2+bxy+cy~2+dx+ey+f=0,根据参数的不同值,可表示成椭圆、双曲线、抛物线等二次曲线.其实除了上述曲线之外,还可表示成两条直线.形如(a_1x+b_1y+c_1)(a_2x+b_2y+c_2)=0的方程也为二元二次方程,可看成退化的二次曲线.
In analytic geometry, we often use the curved beam to solve the problem, such as the intersection of two intersecting lines of straight line beam, the intersection of two circles intersecting the intersection of circular beams, and so on, its greatest role is to simplify the operation. Harness in the application of several aspects of the solution. First, the knowledge combing quadratic equation ax ~ 2 + bxy + cy ~ 2 + dx + ey + f = 0, according to different parameters can be expressed as elliptic, hyperbolic, parabolic In fact, in addition to the above curve, it can be expressed as two straight lines. The equation of (a_1x + b_1y + c_1) (a_2x + b_2y + c_2) = 0 is also a binary quadratic equation, Degenerate quadratic curve.