The coordinates of a point common to a directrix and an asymptote of the hyperbola x225−y216=1 are
(25/41,20/41)
(−25/41,−20/41)
(25/3,20/3)
(−25/3,−20/3)
Equation of the directrices of the given hyperbola
x225−y216=1 are x=±5×525+16=±2541---i
Equations of the asymptotes of the given hyperbola are
x225−y216=0---ii
The points of intersection of Eqs. (i) and (ii) are
(±25/41,±20/41)