Two circles have the following equations #(x -2 )^2+(y -4 )^2= 25 # and #(x +8 )^2+(y +3 )^2= 49 #. 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?

1 Answer
CW
Sep 6, 2016

The two circle do not overlap. The greatest possible distance = 24.2066.

Explanation:

Circle A , centered at (2,4), radius = 5.
Circle B, centered at (-8,-3), radius =7.
Distance from center of circle A to center of circle B :
#=sqrt((-3-4)^2+(-8-2)^2) #
#=sqrt((-7)^2+(-10)^2)#
#=sqrt149 = 12.2066#
since 12.2066 is greater than the sum of the two radii (5+7=12), the two circle do not overlap.
The greatest possible distance bewteen a point on circle A and a point on circle B equals (radius of circle A + distance between the two centers + radius of circle B), which is :
#5+12.2066+7=24.2066#
Hope this helps.

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