Which is a better definition of a parabola?

Question

Based from reading Math books I have this question, hope you can help me Sirs/Madams

Which is a better definition of a simplified parabola

1. A locus of an equation $Cy^2+Dx=0$ or $Ax^2+Ey=0$. (In this definition, definition 2 then becomes a property of the given equations)

or

2.Set of all points in the plane equidistant from a fixed point called focus and a fixed line called directrix

Thanks a lot

Answer 1

Definition 1 is not sufficient to characterize all parabolas in a coordinate plane. It characterizes some--namely, those whose axes of symmetry are coincident with one of the coordinate axes, but for parabolas whose axis of symmetry is not parallel to either coordinate axis, definition 1 is not sufficient.

Consequently, Definition 2 is preferable. There is no restriction on the directrix or focus so long as the latter is not a point on the former.