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# Need Some Help

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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?

Mar 22, 2018

#1
+7601
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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

Mar 22, 2018

#1
+7601
+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