Two circles have the following equations #(x -8 )^2+(y -2 )^2= 36 # and #(x -1 )^2+(y +5 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

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Answer 1 · 2016-10-26T12:14:30

No. #15+7sqrt(2)#

#C_1=(8;2)#; #r_1=6#
#C_2=(1;-5)#; #r_2=9#
#bar(C_1C_2)=sqrt((8-1)^2+(2+5)^2)=7sqrt2>9#
So #C_1# is outside circle 2.

You obtain the maximum possible distance adding
#bar(C_1C_2)+r_1+r_2=15+7sqrt(2)#