Two circles have the following equations: #(x +2 )^2+(y -1 )^2= 49 # and #(x +4 )^2+(y +7 )^2= 25 #. 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?

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Answer 1 · 2017-08-11T18:17:08

The circles overlap and the greatest distance is #=20.25#

The radius of the circles are

#r_A=7#

#r_B=5#

The sum of the radii is

#r_A+r_B=7+5=12#

The centers of the circles are #(-2,1)# and #(-4,-7)#

The distance between the centers is

#d=sqrt((-4-(-2))^2+(-7-(1))^2)#

#=sqrt((-2)^2+(-8)^2)#

#sqrt(4+64)=sqrt68=8.25#

As,

#(r_A+r_B) >d#, the circles overlap

The greatest distance is

#=d+r_A+r_B=12+8.25=20.25#