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关于圆锥曲线中的相交弦有两种常见的表现形式,即两弦相交成直角、两相交弦倾斜角互补.下面分类举例,阐述常用的求解策略.一、两弦相交成直角例1已知直线l:y=kx+1与双曲线C:2x~2-y~2=1的右支交于不同的两点A,B.(1)求实数k的取值范围.(2)是否存在实数k,使得以线段AB为直径的圆经过双曲线C的右焦点F?若存在,求出k的值;若不存在,说明理由.
There are two common forms of intersecting chords in the conic, that is, the two chords intersect at right angles and the two tangent chords are complementary. The following examples are given to illustrate the commonly used strategies. The right branch of line l: y = kx + 1 and hyperbolic line C: 2x ~ 2-y ~ 2 = 1 intersect at two different points A and B. (1) Find the range of real number k (2) There is a real number k, so that the circle with the segment AB as the diameter passes through the right focus F? Of the hyperbola C, if there exists, the value of k is obtained; if not, the reason is explained.