The conic you mentioned above is a shifted parabola .

the full formula is (y+3)^2=4(-1/6)(x+2) and its centre lies at the point P(-2,-3).

a shifted parabola of this type has the formula (y+b)^2=4p(x+a) with p the parameter of the parabola and centre at P(-a,-b)

Minoas

M.R