Two circles have the following equations #(x +5 )^2+(y +6 )^2= 36 # and #(x +2 )^2+(y -1 )^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?

1 Answer
Shwetank Mauria
Apr 9, 2016

Smaller circle is not contained in larger circle and they intersect each other. The greatest possible distance between a point on one circle and another point on the other will be #22.6158#.

Explanation:

First circle has center as #(-5,-6)# and radius #6# and second circle has center as #(-2,1)# and radius #9#.

Distance between circles of two centers is #sqrt((-2-(-5))^2+(1-(-6))^2# or #sqrt(3^2+7^2)=sqrt(9+49)=sqrt58=7.6158#

As the distance between two circles at #7.6158# is less than the sum of their radii #6+9=15# and more than the difference between them at #9-63#, smaller circle is not contained in larger circle and they intersect each other.

The greatest possible distance between a point on one circle and another point on the other will be #6+9+7.6158=22.6158#.

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