# Circle A has a radius of #3 # and a center of #(2 ,4 )#. Circle B has a radius of #2 # and a center of #(4 ,7 )#. If circle B is translated by #<2 ,-4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Jim G.
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Feb 8, 2018

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#"what we have to do here is "color(blue)"compare ""the distance "#

#"(d) between the centres to the "color(blue)"sum of the radii"#

#• " if sum of radii">d" then circles overlap"#

#• " if sum of radii"< d" then no overlap"#

#"we require to find the new centre of B under the given"#

#"translation"#

#(4,7)to(4+2,7-4)to(6,3)larrcolor(red)"new centre of B"#

#"to find d use the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(2,4)" and "(x_2,y_2)=(6,3)#

#d=sqrt((6-2)^2+(3-4)^2)=sqrt(16+1)=sqrt17~~4.123#

#"sum of radii "=3+2=5#

#"since sum of radii">d" then circles overlap"#

graph{((x-2)^2+(y-4)^2-9)((x-6)^2+(y-3)^2-4)=0 [-20, 20, -10, 10]}

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