已知定圆F1:x²+y²+10x+24=0,定圆F2:x²+y²-10x+9=0,动圆M与定圆F1,F2都外切,求动圆圆心M的轨迹方程
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![已知定圆F1:x²+y²+10x+24=0,定圆F2:x²+y²-10x+9=0,动圆M与定圆F1,F2都外切,求动圆圆心M的轨迹方程](/uploads/image/z/5253410-2-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9A%E5%9C%86F1%3Ax%26%23178%3B%2By%26%23178%3B%2B10x%2B24%3D0%2C%E5%AE%9A%E5%9C%86F2%3Ax%26%23178%3B%2By%26%23178%3B-10x%2B9%3D0%2C%E5%8A%A8%E5%9C%86M%E4%B8%8E%E5%AE%9A%E5%9C%86F1%2CF2%E9%83%BD%E5%A4%96%E5%88%87%2C%E6%B1%82%E5%8A%A8%E5%9C%86%E5%9C%86%E5%BF%83M%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B)
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已知定圆F1:x²+y²+10x+24=0,定圆F2:x²+y²-10x+9=0,动圆M与定圆F1,F2都外切,求动圆圆心M的轨迹方程
已知定圆F1:x²+y²+10x+24=0,定圆F2:x²+y²-10x+9=0,动圆M与定圆F1,F2都外切,求动圆圆心M的轨迹方程
已知定圆F1:x²+y²+10x+24=0,定圆F2:x²+y²-10x+9=0,动圆M与定圆F1,F2都外切,求动圆圆心M的轨迹方程
F1:(x+5)^2+y^2=1 F2:(x-5)^2+y^2=4^2
F1圆心(-5,0),半径1,F2圆心(5,0)半径4
设动圆圆心坐标(x,y)
√[(x+5)^2+y^2]-1=√[(x-5)^2+y^2]-4
√[(x+5)^2+y^2]=√[(x-5)^2+y^2]-3 两边平方
x^2+10x+25+y^2=x^2-10x+25+y^2+9-6√[(x-5)^2+y^2]
6√[(x-5)^2+y^2]=9-20x 两边平方
36x^2-360x+900+6y^2=81-360x+400x^2
364x^2-6y^2-819=0