Two circles have the following equations #(x +5 )^2+(y -2 )^2= 36 # 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
Dec 26, 2016
The circles overlap
The greatest possible distance is
Explanation:
We need the equation of a circle, center
The distance between 2 points,
We need to find the distance between the centres of the circles and compare this to the sum of the radii.
The centers are
The distance between the centers is
The sum of the radii is
Therefore,
so,
The circles overlap
The greatest possible distance is
graph{((x+5)^2+(y-2)^2-36)((x+2)^2+(y-1)^2-81)(y-2+1/3(x+5)) = 0 [-19.22, 9.27, -5.39, 8.86]}