Question

我打得有点乱,不过应该看得懂的已知动圆M:x^2+y^2-2mx-2ny+m^2-1=0 与 圆N:x^2+y^2+2x

Answer 1

哪一步不懂?

M

(x-m)^2+(y-n)^2=n^2+1

圆心(m,n),R^2=n^2+1

N

(x+1)^2+(y+1)^2=4

圆心(-1,-1),r=2

圆心距MN

MN^2=(m+1)^2+(n+1)^2

AM=R ,AN=r

R^2=(m+1)^2+(n+1)^2+r^2

n^2+1=m^2+2m+1+n^2+2n+1+4

0=m^2+2m+2n+1+4

(m+1)^2=-2m-4=-2(n+2)

M圆心(m,n),即x=m,y=n

所以(x+1)^2=-2(y+2)

后面

(m+1)^2=-2(n+2)>=0

n+2