Let the focal chord of the parabola P: y^2=4 x along the line L: y= m x+ c, m >0 meet the parabola at the points M and N. Let the line L be a tangent…

Let the focal chord of the parabola $\displaystyle \mathrm{P}: y^2=4 x$ along the line $\displaystyle \mathrm{L}: y=\mathrm{m} x+\mathrm{c}, \mathrm{m}>0$ meet the parabola at the points M and N . Let the line L be a tangent to the hyperbola $\displaystyle \mathrm{H}: x^2-y^2=4$. If O is the vertex of P and F is the focus of H on the positive $\displaystyle x$-axis, then the area of the quadrilateral OMFN is :