Consider a hyperbola H: x^2-2 y^2=4. Let the tangent at a point P (4, √ 6 ) meet the x -axis at Q and latus rectum at R (x_1, y_1), x_1>0. If F is a…

Consider a hyperbola $\displaystyle \mathrm{H}: x^2-2 y^2=4$. Let the tangent at a point $\displaystyle \mathrm{P}(4, \sqrt{6})$ meet the $\displaystyle x$-axis at Q and latus rectum at $\displaystyle \mathrm{R}\left(x_1, y_1\right), x_1>0$. If F is a focus of H which is nearer to the point P , then the area of $\displaystyle \Delta \mathrm{QFR}$ is equal to .