#"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"#

#"before calculating d we require to find the centre of B"#

#"under the given translation"#

#"under the translation "<-4,3>#

#(8,1)to(8-4,1+3)to(4,4)larrcolor(red)"new centre of B"#

#"to calculate 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)=(1,7)" and "(x_2,y_2)=(4,4)#

#d=sqrt((4-1)^2+(4-7)^2)=sqrt(9+9)=sqrt18~~4.24#

#"sum of radii "=1+2=3#

#"since sum of radii"< d" then no overlap"#

#"min. distance "=d-" sum of radii"#

#color(white)(xxxxxxxxxx)=4.24-3=1.24#

graph{((x-1)^2+(y-7)^2-1)((x-4)^2+(y-4)^2-4)=0 [-20, 20, -10, 10]}