If the length of the latus rectum of the ellipse $$x^{2}+4 y^{2}+2 x+8 y-\lambda=0$$ is 4 , and $$l$$ is the length of its major axis, then $$\lambda+l$$ is equal to ____________.

Let the equation of two diameters of a circle $$x^{2}+y^{2}-2 x+2 f y+1=0$$ be $$2 p x-y=1$$ and $$2 x+p y=4 p$$. Then the slope m $$ \in $$ $$(0, \infty)$$ of the tangent to the hyperbola $$3 x^{2}-y^{2}=3$$ passing through the centre of the circle 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 ___________.