The coordinates of a point common to a directrix and an asymptote of the hyperbola x225−y216=1 are

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(25/41,20/41)

(−25/41,−20/41)

(25/3,20/3)

(−25/3,−20/3)

answer is A.

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Detailed Solution

Equation of the directrices of the given hyperbolax225−y216=1 are x=±5×525+16=±2541---iEquations of the asymptotes of the given hyperbola arex225−y216=0---iiThe points of intersection of Eqs. (i) and (ii) are (±25/41,±20/41)

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