Circle A has a radius of #1 # and a center at #(3 ,3 )#. Circle B has a radius of #3 # and a center at #(1 ,7 )#. If circle B is translated by #<2 ,4 >#, 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 coordinates"#
#"of the centre of circle B under the given translation"#
#"which does not change the shape of the circle only"#
#"it's position"#
#"under the translation "<2,4>#
#(1,7)to(1+2,7+4)to(3,11)larrcolor(blue)"new centre of B"#
#"note that the coordinates of the 2 centres have the same"#
#"x-coordinate and so lie on the vertical line "x=3#
#"Hence d is the difference in the y-coordinates"#
#rArrd=11-3=8#
#"sum of radii "=1+3=4#
graph{((x-3)^2+(y-3)^2-1)((x-3)^2+(y-11)^2-9)=0 [-40, 40, -20, 20]}
