Circles A and B have the following equations (x -4 )^2+(y +3 )^2= 9 and (x +4 )^2+(y -1 )^2= 16 . What is the greatest possible distance between a point on circle A and another point on circle B?

1 Answer
Jun 20, 2017

The greatest distance is =15.94

Explanation:

The center of the first circle is =(4,-3) and radius =3

The center of the second circle is =(-4,1) and the radius is =4

The distance between the centers of the circles is

=sqrt((4+4)^2+(-4)^2)= sqrt(64+16)=sqrt80=8.94

This distance is > than the sum of the radii the circles =4+3=7

So, the circles do not overlap.

The greatest distance is located on the line joining the centers of the circles and cutting the circumferences.

The distance is =8.94+3+4=15.94
graph{((x-4)^2+(y+3)^2-9)((x+4)^2+(y-1)^2-16)((y-1)+1/2(x+4))=0 [-11.44, 11.06, -6.48, 4.77]}