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The equation x^2 + y^2 - 4x + 2y = b Describes a circle 

 

1.  Determine the Y coordinate of the center of the circle. 

 

2.  The radius of the circle is 7 units. What is the value of b in the equation?

Guest Mar 22, 2018

Best Answer 

 #1
avatar+7065 
+2

x2 + y2 - 4x + 2y  =  b        We need to get this into standard form. Rearrange the terms.

 

x2 - 4x   + y2 + 2y   =   b        Add  4  and  1  to both sides to complete the squares on the left side.

 

x2 - 4x + 4  + y2 + 2y + 1  =  b + 4 + 1          Factor each perfect square trinomial.

 

(x - 2)(x - 2) + (y + 1)(y + 1)  =  b + 4 + 1

 

(x - 2)2 + (y + 1)2   =   b + 5

 

Now that this is in standard form, we can see that the  y  coordinate of the center is  -1 .

 

And     (the radius)2  =  b + 5       So

 

72  =  b + 5

 

49  =  b + 5

 

44  = b

hectictar  Mar 22, 2018
 #1
avatar+7065 
+2
Best Answer

x2 + y2 - 4x + 2y  =  b        We need to get this into standard form. Rearrange the terms.

 

x2 - 4x   + y2 + 2y   =   b        Add  4  and  1  to both sides to complete the squares on the left side.

 

x2 - 4x + 4  + y2 + 2y + 1  =  b + 4 + 1          Factor each perfect square trinomial.

 

(x - 2)(x - 2) + (y + 1)(y + 1)  =  b + 4 + 1

 

(x - 2)2 + (y + 1)2   =   b + 5

 

Now that this is in standard form, we can see that the  y  coordinate of the center is  -1 .

 

And     (the radius)2  =  b + 5       So

 

72  =  b + 5

 

49  =  b + 5

 

44  = b

hectictar  Mar 22, 2018

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