Two tangent lines $$l_{1}$$ and $$l_{2}$$ are drawn from the point $$(2,0)$$ to the parabola $$2 \mathrm{y}^{2}=-x$$. If the lines $$l_{1}$$ and $$l_{2}$$ are also tangent to the circle $$(x-5)^{2}+y^{2}=r$$, then 17r is equal to ___________.
The sum of diameters of the circles that touch (i) the parabola $$75 x^{2}=64(5 y-3)$$ at the point $$\left(\frac{8}{5}, \frac{6}{5}\right)$$ and (ii) the $$y$$-axis, is equal to ______________.
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 ___________.
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 ______________.