Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 2x^2 + 6y^2 + 5x = 0 A. circle B. parabola C. ellipse D. hyperbola

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Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 2x^2 + 6y^2 + 5x = 0 A. circle B. parabola C. ellipse D. hyperbola

Mathematics
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ellipse.
general eq of conic is \[ax^2+ by^2+2gx+afy+ahxy+c=0\]
conic depends on the sign of \[h^2- ab\]

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Other answers:

ok so negative makes it an ellipse.? 6x2 – 3y2 + 5x – 2y – 7 = 0 would be a hyperbola right or no cause it's negative
2fy*
yes its an ellipse
+ve makes a hyperbola
ok so whats makes something a parabola?
=zero
a parabola bends once; onlyone variable will be squared
oh ok thanks
I guess I just dont get how you tell the difference between a hyperbola and ellipse if they are both negative, like 5x2 – 8y2 + 7x + 3y – 7 = 0 it's not a parabola or circle
that looks like a hyperbola
how do you tell the difference between a hyperbola and ellipse
when x^2 or y^2; only one of them is negative; its a hyperbola usually
if h^2-ab is positive, the conic is a hyperbola
an ellipse/cirlce has the same sign on x^2 and y^2
yes if a n b possess different sign it is usualy a hyperbola
a circle is just a special ellipse
oh ok I get it now thanks very much
just like a square is a special rectangle
right
a hyperbola is an inside out ellipse
oh ok good way to put it

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