Two circles have the following equations: #(x +2 )^2+(y -5 )^2= 16 # and #(x +4 )^2+(y +7 )^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
Dec 23, 2016
No overlapping-
Greatest distance
Explanation:
We calculate the distance between the centers of the circles and we compare this to the sum of the radii.
The centers of the circles are
The radii are
Distance betwwen the center is
The sum of the radii is
Therefore,
So the circles do not overlap.
The greatest distance is
graph{((x+2)^2+(y-5)^2-16)((x+4)^2+(y+7)^2-25)(y-5-6(x+2))=0 [-31.47, 33.5, -13.18, 19.28]}