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Q.

Tangent is drawn at the point $(- 1, 1)$ on the hyperbola $3 x^{2} - 4 y^{2} + 1 = 0$ . The area bounded by the tangent
and the coordinate axes is

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a

$\frac{1}{6}$

b

$\frac{1}{24}$

c

$\frac{1}{12}$

d

$\frac{1}{3}$

answer is C.

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Detailed Solution

Tangent at $(- 1, 1)$ is $S_{1} = 0 \cdot$

$\Rightarrow - 3 x - 4 y + 1 = 0$

It meets $x - a x i s$ at $A (\frac{1}{3}, 0)$ and $y$ -axis at $B (0, \frac{1}{4})$

Area of $Δ O A B = \frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{4} = \frac{1}{24}$

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Tangent is drawn at the point (-1,1) on the hyperbola 3x2-4y2 +1= 0. The area bounded by the tangentand the coordinate axes is