Question: For the circle given in general form write in standard form: X2 +4X+Y2

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Question:
For the circle given in general form write in standard form: X2 +4X+Y2-Y-4=0 So I understand we need to get this in to another form. I am getting stuck on the Y side. I can bring the X side down by taking half of the 4X (2) and squaring it giving me: X2+4X+4 +Y2-Y-4=4 At this point I can get the X side of the Standard Form (X+2)2 + Y2-y-4=4 I am stuck on getting the y in to the Standard formula as well. Particularly with the -Y. Help please!
For the circle given in general form write in standard form: X2 +4X+Y2-Y-4=0 So I understand we need to get this in to another form. I am getting stuck on the Y side. I can bring the X side down by taking half of the 4X (2) and squaring it giving me: X2+4X+4 +Y2-Y-4=4 At this point I can get the X side of the Standard Form (X+2)2 + Y2-y-4=4 I am stuck on getting the y in to the Standard formula as well. Particularly with the -Y. Help please!

Explanation / Answer

x^2 + 4x + y^2 - y - 4 = 0 (x^2 + 4x + 4) + (y^2 - y + 1/4) - 4 = 0 + 4 + 1/4 (x + 2)^2 + (y - 1/2)^2 = 4 + 4 + 1/4 (x + 2)^2 + (y - 1/2)^2 = 8 + 1/4 OR (x + 2)^2 + (y - 1/2)^2 = 33/4 The hint for the -y is that the value of k in (y+k)^2 is 1/2 of the coefficient of the -y, in this case -1/2.

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