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Q.

A tangent drawn to the hyperbola x2a2−y2b2=1 at Pπ6 forms a triangle of area 3a2 sq. units with the coordinate  axes. Then the square of its eccentricity is

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a

15

b

24

c

17

d

14

answer is C.

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Detailed Solution

Pasec⁡π6,btan⁡π6≡P2a3,b3Therefore, the equation of tangent at P is  x3a/2−y3b=1∴ Area of triangle =12×3a2×3b=3a2 or  ba=4 or  e2=1+b2a2=17
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