Two circles have the following equations $(x -2 )^2+(y -4 )^2= 36$ and $(x +8 )^2+(y -7 )^2= 49$ . 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 $(x -2 )^2+(y -4 )^2= 36$ and $(x +8 )^2+(y -7 )^2= 49$ . 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 · 2016-04-19T08:59:17

One circle does not contain the other rather they intersect each other. The greatest possible distance between a point on one circle and another point on the other is $23.44$ .

Explanation:

$(x-2)^2+(y-4)^2=36$ is a circle with center at $(2,4)$ and radius $6$ .

$(x+8)^2+(y-7)^2=49$ is a circle with center at $(-8,7)$ and radius $7$

The distance between centers of two circles is $sqrt((2-(-8))^2+(4-7)^2)$ or $sqrt(10^2+3^2)=sqrt109=10.44$

As the distance between centers is $10.44$ and radius of two circles is $6$ and $7$ but distance is less than sum of radii, one circle does not contain the other rather they intersect each other.

The greatest possible distance between a point on one circle and another point on the other is $10.44+7+6=23.44$ .

graph{((x-2)^2+(y-4)^2-36)((x+8)^2+(y-7)^2-49)=0 [-30, 30, -15, 15]}

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Two circles have the following equations $(x -2 )^2+(y -4 )^2= 36$ and $(x +8 )^2+(y -7 )^2= 49$ . 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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Impact of this question

Science

Math

Humanities

... and beyond

Two circles have the following equations (x -2 )^2+(y -4 )^2= 36 (x -2 )^2+(y -4 )^2= 36 and (x +8 )^2+(y -7 )^2= 49 (x +8 )^2+(y -7 )^2= 49 . 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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Impact of this question

Two circles have the following equations $(x -2 )^2+(y -4 )^2= 36$ and $(x +8 )^2+(y -7 )^2= 49$ . 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?