What is the formula for finding the center of a hyperbola from the general second order?equation.(with xy term)

A plane curve whose rectangular Cartesian coordinates satisfy an algebraic equation of the second degree:

(*)

Equation (*) need not define a real geometrical form, but to preserve generality in such situations one says that it defines an imaginary second-order curve. Depending on the values of the coefficients of the equation (*) it can be transformed by parallel displacement and rotation of the coordinate system through some angle to one of the 9 canonical forms given below, to each of which there corresponds a definite class of curves. Namely,

non-degenerate curves:

, ellipses

, hyperbolas

, parabolas

, imaginary ellipses;

Thank You

Ruchi

Askiitians Faculty