The equations of the directrices of the hyperbola 16x2−9y2=−144 are:
A
y=±825
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B
y=±1625
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C
y=±85
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D
y=±165
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Solution
The correct option is Dy=±165 Theequation16x2−9y2=−144canbewrittenasx29−y216=−1Thisisoftheformx2a2−y2b2=−1So,a2=9,b2=16ora=3,b=4Also,eccentricity(e)=√(1+a2b2)=√1+916=54Theequationsofthedirectricesaregivenby:y=±bey=±4(5/4)=±165