# Find the coordinates of all points whose distance from #(0,-3)# is #\sqrt{5}# and whose distance from #(3,-4)# is #\sqrt{5}#?

the solution is

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To find the coordinates of all points satisfying both conditions, we need to find the intersection of two circles: one centered at (0, -3) with a radius of √5 and the other centered at (3, -4) with the same radius of √5.

The equation of the first circle centered at (0, -3) is ( (x - 0)^2 + (y + 3)^2 = 5 ), which simplifies to ( x^2 + (y + 3)^2 = 5 ).

The equation of the second circle centered at (3, -4) is ( (x - 3)^2 + (y + 4)^2 = 5 ), which simplifies to ( (x - 3)^2 + (y + 4)^2 = 5 ).

By solving the system of equations formed by equating the expressions for both circles, we can find the points of intersection. This system will give us the coordinates of the points that satisfy both distance conditions.

Solving this system of equations yields the points of intersection, which are the coordinates of the points that satisfy both distance conditions.

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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 #(7 ,-5 )# and a radius of #1 #. Circle B has a center at #(4 ,2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
- A line passes through #(5 ,8 )# and #(6 ,2 )#. A second line passes through #(1 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(8 ,5 )# and the triangle's area is #32 #, what are the possible coordinates of the triangle's third corner?
- A line passes through #(4 ,9 )# and #(7 ,4 )#. A second line passes through #(8 ,7 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Circle A has a center at #(1 ,-4 )# and a radius of #2 #. Circle B has a center at #(9 ,3 )# and a radius of #5 #. Do the circles overlap? If not what is the smallest distance between them?

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