Two circles have the following equations (x+5)2+(y+6)2=9 and (x+2)2+(y−1)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
The circles intersect but neither one of them contains the other.
Greatest possible distance
Explanation:
The given equations of the circle are
We start with the equation passing thru the centers of the circle
Using two-point form
After simplification
Solve for the points using first circle and the line
One point at
Another at
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve for the points using second circle and the line
One point at
Another at
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To compute for the farthest distance
Kindly see the graph
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God bless .... I hope the explanation is useful.