Two circles have the following equations: $(x +3 )^2+(y -5 )^2= 64$ and $(x -7 )^2+(y +2 )^2= 81$ . 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?

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Answer 1 · 2017-03-21T07:26:14

The circles overlap and the greatest distance is $=29.2$

The centers of the circle are $(-3,5)$ and $(7,-2)$

The distance between the centers is

$=sqrt((7+3)^2+(-2-5)^2)$

$=sqrt(10^2+7^2)$

$=sqrt(100+49)$

$=sqrt149=12.21$

The radii of the circles are $8$ and $9$

The sum of the radii $=8+9=17$

As the distance between the radii is $<$ than the sum of the radii. the circles overlap.

The greatest disnce is $=12.2+17=29.2$

graph{((x+3)^2+(y-5)^2-64)((x-7)^2+(y+2)^2-81)=0 [-28.85, 28.87, -14.43, 14.45]}

Two circles have the following equations: (x +3 )^2+(y -5 )^2= 64 (x +3 )^2+(y -5 )^2= 64 and (x -7 )^2+(y +2 )^2= 81 (x -7 )^2+(y +2 )^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?