Two circles have the following equations: #(x -1 )^2+(y -4 )^2= 9 # and #(x +6 )^2+(y +9 )^2= 25 #. 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
Andrea B.
Jan 30, 2017

The two circles are external one another and the greatest possible distance is #sqrt 218-8#

Explanation:

The first circle (A) have the centre in Xca=1 nd Yca=4, and its radius is 3.
the second circle (B) has the centre in Xcb=-6 and Ycb=-9. Its radius is 5.
the distance between the centres is:

#d=sqrt ((Xca-XCb)^2 +(Yca-YCb)^2#
#d=sqrt (49+169)=sqrt 218#
the sum of the radii is 3+5 =8 < #sqrt 218#
The two circles are external one another and the greatest possible distance is #sqrt 218-8#

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