Which equation describes a circle?
Identify the conic section with the given equation 5x2-6y2-9x+2y+3=0
p.s. the twos are supposed to be raised to that power
None of those is a circle. In a general quadratic form, if the coefficients of x^2 and y^2 are equal, it's a circle; unequal but the same sign, an ellipse; one zero and one non-zero, a parabola; of different sign, a hyperbola (rectagular if the coefficients are equal in absolute value). So you have a rectangular hyperbola, an ellipse and a parabola respectively.
The quadradic in form of,
can de determined by looking a the relationship between,
In your case we have #2 which is a hyperbola.
[Note: Some cases where not considered such as the coditions for a general quadradic to represent a line or to represent a point]