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Question

If PQ is a double ordinate of the hyperbola x2a2āˆ’y2b2=1 such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola, satisfies

A
1<e<23
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B
e=23
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C
e=32
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D
e>23
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Solution

The correct option is D e>23
If OPQ is equilateral triangle then OP makes 300 with x-axis. (3r2,r2)lies on hyperbola x2a2y2b2=1r2=16a2b212b24a2>012b24a2>0b2a2>412e21>13e2>43e>23

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