Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #2 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

#"circles overlap"#

#"What we have to do here is compare the distance (d) "# #"between the centres to the 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"#
#"under the translation "<-2,2>#
#(5,3)to(5-2,3+2)to(3,5)larrcolor(red)"new centre of B"#
#"to calculate d use the "color(blue)"distance formula"#
#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#"let "(x_1,y_1)=(6,1)" and "(x_2,y_2)=(3,5)#
#d=sqrt((3-6)^2+(5-1)^2)=sqrt(9+16)=sqrt25=5#
#"sum of radii "=4+2=6#
#"since sum of radii">d" then circles overlap"# graph{((x-6)^2+(y-1)^2-16)((x-3)^2+(y-5)^2-4)=0 [-10, 10, -5, 5]}
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Answer 2

No, after the translation, circle B does not overlap with circle A. The minimum distance between points on both circles is the difference between the distance between the centers of the circles and the sum of their radii, which is 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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