# Two circles have the following equations #(x -1 )^2+(y -4 )^2= 64 # and #(x +3 )^2+(y -4 )^2= 9 #. 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

Yes, one circle contains the other.

#### Explanation:

Circle A,

Circle B,

1) calculate d the distance between the centres of the circles, use the distance formula :

where

2) calculate the sum of the radii

Sum of radii =

3) calculate the difference of the radii

Difference of Radii

3 )compare the distance d between the centres of the circles to the sum of the radii and to the difference of the radii.

1) If

2) If

3) If

In our case, since

Hence, Circle B is contained in Circle A.