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Question

The position of the point (5,−4) relative to the hyperbola 9y2−x2=1 is :

A
inside
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B
outside
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C
on the hyberbola
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D
on the directrix of hyperbola
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Solution

The correct option is A inside
Here S(x,y)=9y2x21
and
S(5,4)=9(4)2(5)21=144251=118>0
So the point (5,4) lies inside the hyperbola 9y2x2=1

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