Two circles have the following equations $(x +3 )^2+(y -6 )^2= 64$ 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 · 2017-09-29T17:10:53

The circles overlap

Let the circles be $C_1$ and $C_2$

Let the radius of the circles be $r_1$ and $r_2$

Let the distance between the centers be $=d$

The circles overlap, i.e,

$C_1nnC_2!=O/$

$hArr$

$d<(r_1+r_2)$

Here, we have

$d=sqrt((-7+3)^2+(-2+6)^2)=sqrt(16+16)=sqrt32$

$r_1=8$

$r_2=3$

$r_1+r_2=8+3=11$

$(r_1 +r_2) > d$

The circles overlap

graph{((x+3)^2+(y-6)^2-64)((x+7)^2+(y+2)^2-9)=0 [-32.46, 32.47, -16.23, 16.25]}

Two circles have the following equations (x +3 )^2+(y -6 )^2= 64 (x +3 )^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?