equation is not the equation of a circle

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I can see the following equation is not the equation of a circle because it has a y term and no ${y^2}$ term but how would I better explain this is not an equation of a circle:

${x^2 + 8x -16y -1 = 0}$

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You can make x and y arbitrarily large. (I'd make this a comment, but I don't have enough reputation).