Two circles have the following equations: $(x -1 )^2+(y -4 )^2= 9$ and $(x +6 )^2+(y +9 )^2= 25$ . 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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Two circles have the following equations: $(x -1 )^2+(y -4 )^2= 9$ and $(x +6 )^2+(y +9 )^2= 25$ . 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 · 2017-01-30T05:27:12

The two circles are external one another and the greatest possible distance is $sqrt 218-8$

Explanation:

The first circle (A) have the centre in Xca=1 nd Yca=4, and its radius is 3.
the second circle (B) has the centre in Xcb=-6 and Ycb=-9. Its radius is 5.
the distance between the centres is:

$d=sqrt ((Xca-XCb)^2 +(Yca-YCb)^2$
$d=sqrt (49+169)=sqrt 218$
the sum of the radii is 3+5 =8 < $sqrt 218$
The two circles are external one another and the greatest possible distance is $sqrt 218-8$

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Two circles have the following equations: $(x -1 )^2+(y -4 )^2= 9$ and $(x +6 )^2+(y +9 )^2= 25$ . 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?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Two circles have the following equations: (x -1 )^2+(y -4 )^2= 9 (x -1 )^2+(y -4 )^2= 9 and (x +6 )^2+(y +9 )^2= 25 (x +6 )^2+(y +9 )^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?

1 Answer

Explanation:

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Impact of this question

Two circles have the following equations: $(x -1 )^2+(y -4 )^2= 9$ and $(x +6 )^2+(y +9 )^2= 25$ . 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?