Circles A and B have the following equations (x -4 )^2+(y +3 )^2= 25 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
Alan P.
Oct 4, 2016

color(green)(9+4sqrt(5))

Explanation:

The greatest possible distance will be along the extended line joining the centers of the two circles, between the farthest points of each circle from the other.

Circle A:
(x-4)^2+(y+3)^2=25
color(white)("XXX")has its center at (4,-3)
color(white)("XXX")and a radius of 5

Circle B
(x+4)^2+(y-1)^2=16
color(white)("XXX")has its center at (-4,1)
color(white)("XXX")and a radius of 4

The distance between the two centers is
color(white)("XXX")sqrt((4-(-4))^2+(-3-1)^2)=sqrt(8^2+4^2)=4sqrt(5)

The greatest distance between two points on these circles would be
color(white)("XXX")5+4sqrt(5)+4 = 9+4sqrt(5)

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