Circle A has a radius of #2 # and a center at #(5 ,2 )#. Circle B has a radius of #5 # and a center at #(3 ,4 )#. If circle B is translated by #<2 ,1 >#, 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 radii"#
#• "if sum of radii ">d" then circles overlap"#
#• "if sum of radii "< d" then no overlap of circles"# Before finding d we require to find the coordinates of the 'new' centre of B under the given translation which does not change the shape of the circle only it's position.
#" Under a trans;ation " ((2),(1))#
#(3,4)to(3+2,4+1)to(5,5)larrcolor(red)" new centre of B"# Since the x-ccordinates of both centres are 5 then the centres lie on the same vertical line and d is the difference in their y-coordinates.
#rArrd=5-2=3#
#"sum of radii = radius of A + radius of B "=2+5=7#
#"since sum of radii"> d" then circles overlap"#
graph{(y^2-4y+x^2-10x+25)(y^2-10y+x^2-10x+25)=0 [-13.8, 13.91, -6.93, 6.92]}
