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 ,-3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
Explanation:
What we have to do here is
#color(blue)"compare "# the distance (d) between the centres of the circles 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 'new' "#
#"centre of B under the given translation which does"#
#"not change the shape of the circle only it's position"#
#"under a translation "((2),(-3))#
#(4,7)to(4+2,7-3)to(6,4)larrcolor(red)" new centre of B"#
#"since the centres have the same y-coordinate then"#
#"d is the difference in the x-coordinates"#
#rArrd=6-2=4#
#"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-4)^2-4)=0 [-10, 10, -5, 5]}
