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Question

The equations of the directrices of the hyperbola 16x29y2=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 D y=±165
The equation 16x29y2=144 can bewritten asx29y216=1This is of the form x2a2y2b2=1So, a2=9,b2=16or a=3, b=4Also, eccentricity (e)=(1+a2b2)=1+916=54The equations of the directrices are given by :y=±bey=±4(5/4)=±165

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