# Two circles have the following equations #(x -2 )^2+(y -4 )^2= 36 # and #(x +8 )^2+(y +3 )^2= 49 #. 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

Jul 12, 2017

The circles overlap and the greatest distance is

#### Explanation:

The center of circle

The center of circle

The distance between the centers is

The sum of the radii is

As,

The greatest distance is

graph{((x-2)^2+(y-4)^2-36)((x+8)^2+(y+3)^2-49)(y-4-7/10(x-2))=0 [-32.49, 32.46, -16.24, 16.25]}