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The coordinates of a point common to a directrix and an asymptote of the hyperbola $\frac{x^{2}}{25} - \frac{y^{2}}{16} = 1$ are

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2541,203

2041,−2541

253,203

−2541,2041

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detailed solution

Correct option is D

e2=25+1625⇒e=415Directrix is x=±2541 x=±aeAsymptotes are x225−y216=0So the required coordinates are −2541,2041

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

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The coordinates of a point common to a directrix and an asymptote of the hyperbola $\frac{x^{2}}{25} - \frac{y^{2}}{16} = 1$ are