Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #2 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
May 31, 2018
Explanation:
#"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 the translation "<-2,2>#
#(5,3)to(5-2,3+2)to(3,5)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)=(6,1)" and "(x_2,y_2)=(3,5)#
#d=sqrt((3-6)^2+(5-1)^2)=sqrt(9+16)=sqrt25=5#
#"sum of radii "=4+2=6#
#"since sum of radii">d" then circles overlap"#
graph{((x-6)^2+(y-1)^2-16)((x-3)^2+(y-5)^2-4)=0 [-10, 10, -5, 5]}
