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

Question

amistre64 · Answer

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

amistre64 · Answer

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

isabel☺ · Answer

uhmm...kay maybe with some examples?
oh, wait thanks! :)

amistre64 · Answer

parabola:  y = x^2 + ....

circle:  x^2 + y^2 = 8

ellipse:  4x^2 + 7y^2 = 15

hyperbola:  3x^2 - 2y^2 = 29

isabel☺ · Answer

so why is y=4-x^2 a parabola?

amistre64 · Answer

generally, becasue it has one sqaured term in it

isabel☺ · Answer

but (x-h)^2 = 4p (y-k) is the eq. of a parabola right?

amistre64 · Answer

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