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PLEASEE!!! NEED ASAP!! Which phrase best describes the graph of this equation? x^2+y^2+2y-2=0 A. a parabola that opens up B. a circle with a center at C. a parabola that opens to the right D. a circle with a center at

User Andrei N
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The graph of the equation x^2+y^2+2y-2=0 can be described as a circle with a center at (0,-1).

To understand why, let's simplify the equation by completing the square.

First, rearrange the terms:

x^2 + (y^2 + 2y) = 2

Next, focus on the term involving y. To complete the square, we need to add and subtract the square of half of the coefficient of y, which is 1:

x^2 + (y^2 + 2y + 1 - 1) = 2

Simplifying this equation further, we have:

x^2 + (y+1)^2 - 1 = 2

Now, move the constant term to the right side of the equation:

x^2 + (y+1)^2 = 3

Comparing this equation to the standard form of a circle, (x-h)^2 + (y-k)^2 = r^2, we can determine that the center of the circle is at the point (h, k). In this case, the center is (0, -1).

Therefore, the correct answer is B. a circle with a center at (0, -1)

User Donnikitos
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