Two circles have the following equations $(x -1 )^2+(y -6 )^2= 64$ and $(x +7 )^2+(y +2 )^2= 9$ . 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 · 2016-10-16T22:26:52

One does not contain the other.
The greatest distance possible is $8sqrt(2) + 11$

The radius of the first circle is 8
The radius of second circle is 3

The center of the first circle is $(1, 6)$
The center of the second circle is $(-7, -2)$
The distance, d, between their centers is:

$d = sqrt((1 - -7)^2 + (6 - -2)^2$

$d = 8sqrt(2)$

This is greater than the sum of their radii so they do not touch.

Two circles have the following equations (x -1 )^2+(y -6 )^2= 64 (x -1 )^2+(y -6 )^2= 64 and (x +7 )^2+(y +2 )^2= 9 (x +7 )^2+(y +2 )^2= 9 . 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?