Canonical equations of ellipse, parabola and hyperbola are well-known.
But I have hard times trying to find those three equations for an ellipse, parabola and hyperbola in any place of $(2D)$ coordinate plane and rotated by a given angle.
Could anyone please help to summarize those three equations with parameters, so that those parameters allow to draw moved and rotated ellipse, parabola and hyperbola in $XY$ plane?