∫ the distance from the focus F(c, 0) to the corresponding directrix x = a 2/c p = c-a 2/c = (c 2-a 2)/c = b 2/c.

∴b^2=pc

Eccentricity e=c/a

∴c=ae

∴a^2=c^2-b^2=a^2e^2-pc

∴(e^2- 1)a^2=pc=pae

∴(e^2- 1)a=pe

∴ The real semi-axis length of hyperbola A = EP/(E 2- 1)