As for the type of equation, it is a quadratic polynomial in two variables. If what you really meant was: "What type of conic section curve is represented by the graph of the given equation?" -- that is a different matter altogether.
You have both x-squared and y-squared terms, therefore NOT a parabola,
You have different magnitude coefficients on the x-squared and y-squared terms, therefore NOT a circle.
The x-squared and y-squared terms have the same sign, therefore NOT a hyperbola.
