Show that the equation represents a circle by rewriting it in standard form, and find the center and the radius of the circle.

x^2+y^2+4x+y+4=0

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Rewrite this as .....   x^2 + 4x +y^2 + y = -4

Now, we need to "complete the square" on x and y......(review how to do this if you don't remember)....

x^2 + 4x + 4   +  y^2 + y + 1/4 =  - 4 + 4 + 1/4

(x+2)^2 + (y+ 1/2)^2 =  1/4

The center is ( -2, -1/2)  and the radius is 1/2