圆C1:x²+y²+2mx+4y+m²-5=0,圆C2:x²+y²-2x-2my+m²-3=0.(1)若两圆相外切,求出此时m的值及两圆外公切线长.(2)是否存在m时使两圆相交,若存在,求出m的范围,若不存在,说明理由.
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![圆C1:x²+y²+2mx+4y+m²-5=0,圆C2:x²+y²-2x-2my+m²-3=0.(1)若两圆相外切,求出此时m的值及两圆外公切线长.(2)是否存在m时使两圆相交,若存在,求出m的范围,若不存在,说明理由.](/uploads/image/z/2487408-24-8.jpg?t=%E5%9C%86C1%EF%BC%9Ax%26%23178%3B%2By%26%23178%3B%2B2mx%2B4y%2Bm%26%23178%3B-5%3D0%2C%E5%9C%86C2%EF%BC%9Ax%26%23178%3B%2By%26%23178%3B-2x-2my%2Bm%26%23178%3B-3%3D0.%EF%BC%881%EF%BC%89%E8%8B%A5%E4%B8%A4%E5%9C%86%E7%9B%B8%E5%A4%96%E5%88%87%2C%E6%B1%82%E5%87%BA%E6%AD%A4%E6%97%B6m%E7%9A%84%E5%80%BC%E5%8F%8A%E4%B8%A4%E5%9C%86%E5%A4%96%E5%85%AC%E5%88%87%E7%BA%BF%E9%95%BF.%EF%BC%882%EF%BC%89%E6%98%AF%E5%90%A6%E5%AD%98%E5%9C%A8m%E6%97%B6%E4%BD%BF%E4%B8%A4%E5%9C%86%E7%9B%B8%E4%BA%A4%2C%E8%8B%A5%E5%AD%98%E5%9C%A8%2C%E6%B1%82%E5%87%BAm%E7%9A%84%E8%8C%83%E5%9B%B4%2C%E8%8B%A5%E4%B8%8D%E5%AD%98%E5%9C%A8%2C%E8%AF%B4%E6%98%8E%E7%90%86%E7%94%B1.)
圆C1:x²+y²+2mx+4y+m²-5=0,圆C2:x²+y²-2x-2my+m²-3=0.(1)若两圆相外切,求出此时m的值及两圆外公切线长.(2)是否存在m时使两圆相交,若存在,求出m的范围,若不存在,说明理由.
圆C1:x²+y²+2mx+4y+m²-5=0,圆C2:x²+y²-2x-2my+m²-3=0.(1)若两圆相外切,求出此时m的值及两圆外公切线长.(2)是否存在m时使两圆相交,若存在,求出m的范围,若不存在,说明理由.
圆C1:x²+y²+2mx+4y+m²-5=0,圆C2:x²+y²-2x-2my+m²-3=0.(1)若两圆相外切,求出此时m的值及两圆外公切线长.(2)是否存在m时使两圆相交,若存在,求出m的范围,若不存在,说明理由.
C1:(x+m)^2+(y+2)^2=3^2
C2:(x-1)^2+(y-m)^2=2^2
⑴、两圆外切,则两圆心间距离=5,
(m+1)^2+(2+m)^2=25
m^2+2 m+1+4+4m+m^2=25
2m^2+6m-20=0
m^2+3m-10=0
m=2或m=-5
外公切线长=✓(5^2-1^2)=2✓6
⑵、两圆相交,两圆心距离大于1小于5,
m^2+3m-10