Question

what is nonzero abscissa,nonzero ordinate

Answer 1

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Is this what you mean??
The abscissa is the "x" coordinate, the ordinate is the "y" coordinate. Non-zero "x" would include all x points EXCEPT those on the "y" axis. Negative "y" would be all y values below the x axis.
Therefore, it would be all coordinates in quadrants 3 & 4 of a Cartesian plane which do not lie on either axis.

Answer 2

The horizontal or x coordinate on an (x, y) graph; the input of a function against which the output is plotted.
The vertical or y coordinate is the " ordinate".