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?
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
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