Circle A has a radius of #3 # and a center of #(8 ,5 )#. Circle B has a radius of #2 # and a center of #(6 ,1 )#. If circle B is translated by #<2 ,7 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
circles overlap.
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, require to find the 'new' centre of circle B under the given transformation which does not change the shape of the circle only it's position.
Under a translation of
#((2),(7))#
#(6,1)to(6+2,1+7)to(8,8)larr" new centre of B "# To calculate d, in this case since the coordinates of the centres (8 ,5) and (8 ,8) have the same x-coordinate- that is they lie on the same vertical line, then d is the difference in the y-coordinates.
#rArrd=8-5=3# Sum of radii = radius of A + radius of B = 3 + 2 + 5
Since sum of radii > d , then the circles overlap
graph{(y^2-10y+x^2-16x+80)(y^2-16y+x^2-16x+124)=0 [-28.48, 28.48, -14.22, 14.26]}
