Circles A and B have the following equations $(x -4 )^2+(y +3 )^2= 25$ and $(x +4 )^2+(y -1 )^2= 49$ . What is the greatest possible distance between a point on circle A and another point on circle B?

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Circles A and B have the following equations $(x -4 )^2+(y +3 )^2= 25$ and $(x +4 )^2+(y -1 )^2= 49$ . What is the greatest possible distance between a point on circle A and another point on circle B?

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Answer 1 · 2016-05-21T16:46:44

$d = 20.9443$

Explanation:

Circles $C_1$ and $C_2$ have respectively centers at
$p_1=(4,-3), p_2=(-1,1)$ and radius $r_1=5, r_2=7$
Their distance concerning centers is given by
$d_{12} = norm (p_1-p_2) = 8.94427$ .

As we can observe is verified that
$r_1 < r_2 + norm (p_1-p_2)$
$r_2 < r_1 + norm (p_1-p_2)$
$norm (p_1-p_2) < r_1 + r_2$
so the circles intersect in two points.
In this case the maximum distance between $C_1$ and $C_2$ is given by
$norm (p_1-p_2) +r_1+r_2 = 20.9443$

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Circles A and B have the following equations $(x -4 )^2+(y +3 )^2= 25$ and $(x +4 )^2+(y -1 )^2= 49$ . What is the greatest possible distance between a point on circle A and another point on circle B?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Circles A and B have the following equations (x -4 )^2+(y +3 )^2= 25 (x -4 )^2+(y +3 )^2= 25 and (x +4 )^2+(y -1 )^2= 49 (x +4 )^2+(y -1 )^2= 49 . What is the greatest possible distance between a point on circle A and another point on circle B?

1 Answer

Explanation:

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Circles A and B have the following equations $(x -4 )^2+(y +3 )^2= 25$ and $(x +4 )^2+(y -1 )^2= 49$ . What is the greatest possible distance between a point on circle A and another point on circle B?