If the Directrix is negative then the Focus will have a positive sign?
Example:
Directrix: $\displaystyle x=-5$ then Focus$\displaystyle (5,0)$
Am I right, or the sign remains the same?
This doesn't seem to always be true. The focus and directrix are equidistant from the vertex when connecting the three in a line. Consider a basic case where the standard parabola of y=x^2 was vertically shifted up 30 units. The focus is slightly above the vertex and the directrix is a horizontal line running slightly below the vertex but both are always positive.