# Two circles have the following equations #(x +5 )^2+(y +3 )^2= 9 # and #(x +4 )^2+(y -1 )^2= 1 #. 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?

No overlap of the circles. Greatest distance

Circle A, center (-5,-3),

Circle B, center (-4,1),

Now compare the distance

1) If the sum of the radii

2) If the sum of the radii

3)If the difference of the radii

To calculate

where

here the two points are

let

Sum of radii = radius of A + radius of B

Since sum of radius

greatest distance :

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The two 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 calculating the distance between their centers and then adding their radii. The distance between the centers of the circles can be found using the distance formula. Let's denote the centers of the circles as ((x_1, y_1)) and ((x_2, y_2)). Then the distance between their centers is given by:

[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}]

Once you have the distance between the centers, add the radius of one circle to the distance to find the greatest possible distance between a point on one circle and another point on the other.

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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.

- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(pi)/2 #, and the triangle's area is #2 #. What is the area of the triangle's incircle?
- A circle has a center that falls on the line #y = 1/7x +4 # and passes through # ( 7 ,8 )# and #(3 ,6 )#. What is the equation of the circle?
- A circle has a chord that goes from #( 2 pi)/3 # to #(17 pi) / 12 # radians on the circle. If the area of the circle is #9 pi #, what is the length of the chord?
- A circle has a chord that goes from #( 4 pi)/3 # to #(17 pi) / 12 # radians on the circle. If the area of the circle is #27 pi #, what is the length of the chord?
- Find the equation of a circle, which passes through origin and has #x#-intercept as #3# and #y#-intercept as #4#? What would have been the equation, if intercepts are reversed?

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