"what we have to do here is compare the distance (d)"
"between the centres to the 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 new centre"
"of B under the given translation"
"under a translation "< -2,2>
(5,7)to(5-2,7+2)to(3,9)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)=(6,2)" and "(x_2,y_2)=(3,9)
d=sqrt((3-6)^2+(9-2)^2)=sqrt(9+49)=sqrt58~~7.62
"sum of radii "=4+3=7
"since sum of radii"< d" then no overlap"
"minimum distance "=d-" sum of radii"
color(white)(xxxxxxxxxxxxx)=7.62-7=0.62
graph{((x-6)^2+(y-2)^2-16)((x-3)^2+(y-9)^2-9)=0 [-20, 20, -10, 10]}