Circles A and B have the following equations #(x -4 )^2+(y +3 )^2= 9 # and #(x +4 )^2+(y -1 )^2= 16 #. What is the greatest possible distance between a point on circle A and another point on circle B?

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Answer 1 · 2017-06-20T18:45:11

The greatest distance is #=15.94#

The center of the first circle is #=(4,-3)# and radius #=3#

The center of the second circle is #=(-4,1)# and the radius is #=4#

The distance between the centers of the circles is

#=sqrt((4+4)^2+(-4)^2)= sqrt(64+16)=sqrt80=8.94#

This distance is #># than the sum of the radii the circles #=4+3=7#

So, the circles do not overlap.

The greatest distance is located on the line joining the centers of the circles and cutting the circumferences.

The distance is #=8.94+3+4=15.94#
graph{((x-4)^2+(y+3)^2-9)((x+4)^2+(y-1)^2-16)((y-1)+1/2(x+4))=0 [-11.44, 11.06, -6.48, 4.77]}