Problem :
Is the following conic a parabola, an ellipse, a circle, or a
hyperbola: -3x2 + y + 2 = 0?
It is a parabola.
Problem :
Is the following conic a parabola, an ellipse, a circle, or a hyperbola: 2x2 +3xy - 4y2 + 2x - 3y + 1 = 0?
It is a hyperbola.
Problem :
Is the following conic a parabola, an ellipse, a circle, or a hyperbola: 2x2 -3y2 = 0?
It is a hyperbola.
Problem :
Is the following conic a parabola, an ellipse, a circle, or a hyperbola: -3x2 + xy - 2y2 + 4 = 0?
It is an ellipse or a circle.
Problem :
Is the following conic a parabola, an ellipse, a circle, or a hyperbola: x = 0?
It is a degenerate conic.
x = 0 is a line.