can a parabolic curve be offsetted and yet remain a parabola?

Question

Hello,



Suppose we make a co-ordinate system with y and x axes.locate a point 5 units above the vertex which is at the ORIGIN.this point is the focus.now, we make a dashed line 5 units below parallel to y=0 and this is our directrix.considering this origin we sketch a parabola according to the equation y2=4fx where f is the focus.lets call this parabola 1

NOW,the question is.i intend to OFFSET the parabola 1 curve 2 units BELOW.such that the new curve(i am keeping it un named and un-defined and ambigious by calling it a curve) i get is 2 units exactly below the parabola 1 with the same curvature(similar to offseting a line or a semi-circle in a CAD modelling software such as pro-e or SW).WILL THIS NEW CURVE BE A PARABOLA (as per its definition of equal distances from directrix and focus)???

Answer 1

I do this offset on a cad system easily,

yes it will be the same parabola

Answer 2

I have no idea what offsetting means but you can translate the parabola vertically and it will have the same shape. Because the distances from vertex to focus and vertex to directrix are not the same, they can not be the focus and directrix of the new parabola.