Consider a hyperbola \( \mathrm{H}: x^{2}-2 y^{2}=4 \). Let the tan...

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Consider a hyperbola \( \mathrm{H}: x^{2}-2 y^{2}=4 \). Let the tangent at a point \( P(4, \sqrt{6}) \) meet the \( x \)-axis at \( Q \) and latus rectum
\( \mathrm{P} \) at \( R\left(x_{1}, y_{1}\right), x_{1} \geq 0 \). If \( F \) is a focus of \( H \) which is nearer to the point \( P \), then the area of \( \triangle Q F R \) is equal to :
(a) \( \sqrt{6}-1 \)
(b) \( \frac{7}{\sqrt{6}}-2 \)
(c) \( 4 \sqrt{6}-1 \)
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