# Circle A has a center at #(-1 ,1 )# and a radius of #2 #. Circle B has a center at #(3 ,-2 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?

The circles do not overlap and are separated by a minimum distance of

The length of the line segment joining the centers of the two circles is:

Circle A covers

circle B covers

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Yes, the circles overlap. The smallest distance between the circles occurs at the point where the line segment connecting the centers of the circles intersects both circles. This distance can be calculated using the distance formula between two points. The distance between the centers of the circles is √((3 - (-1))^2 + (-2 - 1)^2) = √((4)^2 + (-3)^2) = √(16 + 9) = √25 = 5 units. Subtracting the sum of the radii from this distance gives us the smallest distance between the circles: 5 - (2 + 1) = 5 - 3 = 2 units. Therefore, the smallest distance between the circles is 2 units.

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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.

- Circle A has a center at #(-4 ,2 )# and a radius of #3 #. Circle B has a center at #(2 ,-1 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(4 ,9 )# to #(8 ,5 )# and the triangle's area is #48 #, what are the possible coordinates of the triangle's third corner?
- Circle A has a center at #(4 ,-1 )# and a radius of #3 #. Circle B has a center at #(-3 ,6 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
- Circle A has a center at #(5 ,-2 )# and a radius of #2 #. Circle B has a center at #(4 ,6 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?
- What is the slope-intercept form of the equation of the line through the point (-8, 7) and parallel to the line: #x + y = 13#?

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