A tangent drawn to hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ at $P (\frac{π}{6})$ froms a triangle of area $3 a^{2}$ square units, with the coordinate axes, then the square of its eccentricity is (A) $15$ (B) $24$ (C) $17$ (D) $14$

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A tangent drawn to hyperbola

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

P (\frac{π}{6})

froms a triangle of area

3 a^{2}

square units, with the coordinate axes, then the square of its eccentricity is (A)

15

(B)

24

(C)

17

(D)

14

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Question Text

A tangent drawn to hyperbola

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

P (\frac{π}{6})

froms a triangle of area

3 a^{2}

square units, with the coordinate axes, then the square of its eccentricity is (A)

15

(B)

24

(C)

17

(D)

14

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