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
Narad T.
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

=√(4+4)2+(−4)2=√64+16=√80=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]}

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