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how will you know if an equation is a parabola, circle, etc.?

Mathematics
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there is a general conic equation; something like x^2 + xy + y^2 + ... that i can never recall if its a standard conic (not twisted at an angle) you can recognize certain proerties
a parabola only has one square in it a circle will have the same constants for x^2 and y^2, and have a + in the middle an ellipse is like a circle, but it has different constants a hyperbola is like an ellipse, but with a minus sign
uhmm...kay maybe with some examples? oh, wait thanks! :)

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Other answers:

parabola: y = x^2 + .... circle: x^2 + y^2 = 8 ellipse: 4x^2 + 7y^2 = 15 hyperbola: 3x^2 - 2y^2 = 29
so why is y=4-x^2 a parabola?
generally, becasue it has one sqaured term in it
but (x-h)^2 = 4p (y-k) is the eq. of a parabola right?
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there is an algebra definition and a geometric definition; you presented the geometric one
what's the difference between those definition ?
one is defined by geometric properties, while te other is defined by arithmetical properties. The two are equivalent, but its just the perspective studies that generated them.
directrix distance (directrix is a geometric property) v v (x-h)^2 = 4p (y-k) ^ ^ ^ ^ center x center y
y = 4 -x^2 x^2 = 4 - y (x - 0)^2 = -4/4 (y - 4) p = -1/4; and center (or vertex in this case) is at (0,4)
cost accting exam starting soon, good luck ;)
thanks! :)

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