已知圆M和圆P:x2+y2-22x-10=0相内切,且过定点Q(-2,0).(Ⅰ)求动圆圆心...

发布网友 发布时间：2024-10-24 16:12

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热心网友 时间：2024-10-28 02:39

（I）由已知|MP|=23-|MQ|，即|MP|+|MQ|=23，…（2分）
且23大于|PQ|，…（3分）
所以M的轨迹是以（-2，0），（2，0）为焦点，23为长轴长的椭圆，
即其方程为x23+y2＝1．…（5分）
（II）设AB的方程为y=kx+t，
代入椭圆方程得到（3k2+1）x2+6ktx+3t2-3=0，
△=4（9k2+3-3t2）＞0，即3k2+1＞t2，①方程有两个不同的解，…（6分）
x1+x2＝?6kt3k2+1，x1+x22＝?3kt3k2+1，
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