Two circles have the following equations ${(x - 8)}^{2} + {(y - 2)}^{2} = 36$ $(x -8 )^2+(y -2 )^2= 36$ and ${(x - 1)}^{2} + {(y + 5)}^{2} = 81$ $(x -1 )^2+(y +5 )^2= 81$ . 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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Two circles have the following equations ${(x - 8)}^{2} + {(y - 2)}^{2} = 36$ $(x -8 )^2+(y -2 )^2= 36$ and ${(x - 1)}^{2} + {(y + 5)}^{2} = 81$ $(x -1 )^2+(y +5 )^2= 81$ . 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 · 2016-10-26T12:14:30

No. $15 + 7 \sqrt{2}$ $15+7sqrt(2)$

Explanation:

$C_{1} = (8; 2)$ $C_1=(8;2)$ ; $r_{1} = 6$ $r_1=6$
$C_{2} = (1; - 5)$ $C_2=(1;-5)$ ; $r_{2} = 9$ $r_2=9$
$¯ ¯¯¯¯¯¯¯ ¯ C_{1} C_{2} = \sqrt{{(8 - 1)}^{2} + {(2 + 5)}^{2}} = 7 \sqrt{2} > 9$ $bar(C_1C_2)=sqrt((8-1)^2+(2+5)^2)=7sqrt2>9$
So $C_{1}$ $C_1$ is outside circle 2.

You obtain the maximum possible distance adding
$¯ ¯¯¯¯¯¯¯ ¯ C_{1} C_{2} + r_{1} + r_{2} = 15 + 7 \sqrt{2}$ $bar(C_1C_2)+r_1+r_2=15+7sqrt(2)$

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Two circles have the following equations (x−8)2+(y−2)2=36(x -8 )^2+(y -2 )^2= 36 and (x−1)2+(y+5)2=81(x -1 )^2+(y +5 )^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?

1 Answer

Explanation:

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