What is the conic for 4x^2-8x+144y+36y^2+4?

What is the conic for 4x^2-8x+144y+36y^2+4?

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We can write this as:

4x^2-8x+144y+36y^2  = -4          Dividing through by 4, we have

x^2 - 2x + 9y^2 + 36y = -1          Completing the suare on x and y, we have

(x^2 - 2x +1) + 9(y^2 + 4y +4) = -1  + 1 +36    Factoring, we have

(x - 1)^2   +9(y + 2)^2   =   36     Dividing though by 36, we have

[(x - 1)^2] / 36   + [(y + 2)^2] / 4   =   1

So we have an ellipse centered at (1, -2)  with a = 6 (the semi-major axis) and b = 2 (the semi-minor axis).

There is no equal sign ?????  CPhill has assumed it equals 0 

The general equation for any conic section is

Here, we have no "xy" term  (which would indicate a "rotated conic")

I'd be happy for some more thought/discussion on this one but i think I am too tired tonight.

I might think about it tomorrow.