高中《解析几何》(甲)P·103第17题所讨论的方程 x~2/(9-k)+y~2/(4-k)=1实质上是一个共焦点(±5~(1/2),0)的有心二次曲线系。1989年数学高考文科第(24)题讨论了这类曲线系的一个性质(见例4)。一般地,共焦点(c,0),(-c,0)(c>0)的有心二次曲线系可以表示为或性质1 除两轴外,平面上每一点都有共焦二次曲线系中的一个椭圆和一个双曲线 The equation x~2/(9-k)+y~2/(4-k)=1 discussed in Question 17 of High School Analytic Geometry (A) P.103 is essentially a confocal point (±5~ 1/2),0) The centered quadratic curve system. The 1989 mathematics entrance examination subject (24) discusses a property of this type of curve system (see Example 4). In general, a concentric quadratic curve system of confocal (c, 0), (-c, 0) (c>0) can be expressed as or a property of 1; in addition to two axes, there is a confocal quadratic curve at each point in the plane. An ellipse and a hyperbola in the system