Two circles have the following equations: #(x +6 )^2+(y -1 )^2= 49 # and #(x -9 )^2+(y -4 )^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
Feb 18, 2017
The circles overlap and the greatest distance is
Explanation:
We compare the sum of the radii to the distance between the centers,
Radius of first circle
Radius of second circle
The center of the first circle is
The center of the second circle is
The distance between the centers is
Therefore,
So,
the circles overlap
The greatest distance is
graph{((x+2)^2+(y-1)^2-49)((x-9)^2+(y-4)^2-81)(y-4-1/5(x-9))=0 [-22.8, 22.83, -11.4, 11.4]}