圆C1:x²+y²-2x-6y-1=0,圆C2:x²+y²-10x-12y+m=0.求m为何值时,圆C1与圆C2外切?
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![圆C1:x²+y²-2x-6y-1=0,圆C2:x²+y²-10x-12y+m=0.求m为何值时,圆C1与圆C2外切?](/uploads/image/z/6074803-19-3.jpg?t=%E5%9C%86C1%EF%BC%9Ax%26%23178%3B%2By%26%23178%3B-2x-6y-1%3D0%2C%E5%9C%86C2%EF%BC%9Ax%26%23178%3B%2By%26%23178%3B-10x-12y%2Bm%3D0.%E6%B1%82m%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2C%E5%9C%86C1%E4%B8%8E%E5%9C%86C2%E5%A4%96%E5%88%87%3F)
圆C1:x²+y²-2x-6y-1=0,圆C2:x²+y²-10x-12y+m=0.求m为何值时,圆C1与圆C2外切?
圆C1:x²+y²-2x-6y-1=0,圆C2:x²+y²-10x-12y+m=0.求m为何值时,圆C1与圆C2外切?
圆C1:x²+y²-2x-6y-1=0,圆C2:x²+y²-10x-12y+m=0.求m为何值时,圆C1与圆C2外切?
化简(x-1)²+(y-3)²=11 ,(x-5)²+(y-6)²=61-m
C1(1,3)C2(5,6)
C1C2=5
∵圆C1与圆C2外切
r1=√11,r2=√(61-m)
C1C2=r1+r2=5
m=25+10√11