Question

Which conic section does this equation represent?
x^2-4x-y^2+6y-9=5

Parabola
Ellipse
Hyperbola
Circle

Answer 1

hyperbola. Since both x and y are squared, and one has a negative coefficient, it has to be a hyperbola.

Answer 2

The conic section has a negative squared term, so it's a hyperbola.
Just look at the squared terms, x^2 and y^2.
Both have the same coefficient and are both positive: Circle
Both are positive but different coefficients: Ellipse
One is negative and one is positive: Hyperbola
There is only one squared term: Parabola.