Here's a detailed and educational solution to the problem, broken down into clear steps.

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

1. Understanding the Hyperbola and its Parameters

The first step in any problem involving conic sections is to bring the given equation into its standard form. This allows us to easily identify key parameters like $a