# Two circles have the following equations #(x -1 )^2+(y -6 )^2= 64 # and #(x +7 )^2+(y +2 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

One does not contain the other.

The greatest distance possible is

The radius of the first circle is 8 The radius of second circle is 3

This is greater than the sum of their radii so they do not touch.

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The circles do not contain each other. The greatest possible distance between a point on one circle and another point on the other can be found by determining the distance between their centers and subtracting the sum of their radii.

Center of the first circle: (1, 6)

Center of the second circle: (-7, -2)

Radius of the first circle: √64 = 8

Radius of the second circle: √9 = 3

Distance between the centers = √[(1 - (-7))^2 + (6 - (-2))^2] = √[64 + 64] = √128 = 8√2

Greatest possible distance = Distance between centers - (radius of first circle + radius of second circle)

= 8√2 - (8 + 3)

= 8√2 - 11

So, the greatest possible distance between a point on one circle and another point on the other is (8\sqrt{2} - 11).

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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.

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