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$A tangent drawn to the hyperbola \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 at P (\frac{π}{6}) forms a triangle of area 3 a^{2} sq. units with the coordinate$
$axes. Then the square of its eccentricity is$

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Correct option is C

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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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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$A tangent drawn to the hyperbola \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 at P (\frac{π}{6}) forms a triangle of area 3 a^{2} sq. units with the coordinate$
$axes. Then the square of its eccentricity is$