Two circles have the following equations: $(x +2 )^2+(y -5 )^2= 16$ and $(x +4 )^2+(y +7 )^2= 25$ . 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?

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Answer 1 · 2016-12-23T05:15:09

No overlapping-
Greatest distance $=21.17$

We calculate the distance between the centers of the circles and we compare this to the sum of the radii.

The centers of the circles are $(-2,5)$ and $(-4,-7)$

The radii are $=4$ and $=5$

Distance betwwen the center is

$d=sqrt((-4--2)^2+(-7-5)^2)$

$d=sqrt(4+144)=sqrt148=12.17$

The sum of the radii is $s=4+5=9$

Therefore,

$d>s$

So the circles do not overlap.

The greatest distance is $=s+d=9+12.17=21.17$

graph{((x+2)^2+(y-5)^2-16)((x+4)^2+(y+7)^2-25)(y-5-6(x+2))=0 [-31.47, 33.5, -13.18, 19.28]}

Two circles have the following equations: (x +2 )^2+(y -5 )^2= 16 (x +2 )^2+(y -5 )^2= 16 and (x +4 )^2+(y +7 )^2= 25 (x +4 )^2+(y +7 )^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?