"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]}