Circle A has a center at #(-5 ,8 )# and a radius of #4 #. Circle B has a center at #(-3 ,3 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
1 Answer
Explanation:
What we have to do here is
#color(blue)"compare"# the distance (d) between the centres of the circles with the#color(blue)"sum of the radii"# • If sum of radii > d , then circles overlap
• If sum of radii < d , then no overlap
To calculate d, use the
#color(blue)"distance formula"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))#
where# (x_1,y_1),(x_2,y_2)" are 2 coordinate points"#
#"the 2 points here are " (-5,8)" and " (-3,3)#
#"let " (x_1,y_1)=(-5,8)" and " (x_2,y_2)=(-3,3)#
#d=sqrt((-3+5)^2+(3-8)^2)=sqrt(4+25)=sqrt29≈5.385#
#"sum of radii = radius of A + radius of B = 4+4= 8"# #Since sum of radii > d , then circles overlap.
graph{(y^2-16y+x^2+10x+73)(y^2-6y+x^2+6x+2)=0 [-28.48, 28.47, -14.24, 14.24]}