Let PQ be a focal chord of length 6.25 units of the parabola y² = 4x. If O is the vertex of the parabola, then 10 times the area (in sq. units) of $$\Delta$$POQ is equal to ___________.

Let $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $$4(2\sqrt 2 + \sqrt {14} )$$. If the eccentricity H is $${{\sqrt {11} } \over 2}$$, then the value of a² + b² is equal to __________.

A circle of radius 2 unit passes through the vertex and the focus of the parabola y² = 2x and touches the parabola $$y = {\left( {x - {1 \over 4}} \right)^2} + \alpha $$, where $$\alpha$$ > 0. Then (4$$\alpha$$ $$-$$ 8)² is equal to ______________.

Let a line L₁ be tangent to the hyperbola $${{{x^2}} \over {16}} - {{{y^2}} \over 4} = 1$$ and let L₂ be the line passing through the origin and perpendicular to L₁. If the locus of the point of intersection of L₁ and L₂ is $${({x^2} + {y^2})^2} = \alpha {x^2} + \beta {y^2}$$, then $$\alpha$$ + $$\beta$$ is equal to _____________.