Let a tangent to the curve $$9{x^2} + 16{y^2} = 144$$ intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is ________

Let the tangents at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ on the ellipse $$\frac{x^{2}}{2}+\frac{y^{2}}{4}=1$$ meet at the point $$R(\sqrt{2}, 2 \sqrt{2}-2)$$. If $$\mathrm{S}$$ is the focus of the ellipse on its negative major axis, then $$\mathrm{SP}^{2}+\mathrm{SQ}^{2}$$ is equal to ___________.

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 ____________.

If two tangents drawn from a point ($$\alpha$$, $$\beta$$) lying on the ellipse 25x^{2} + 4y^{2} = 1 to the parabola y^{2} = 4x are such that the slope of one tangent is four times the other, then the value of (10$$\alpha$$ + 5)^{2} + (16$$\beta$$^{2} + 50)^{2} equals ___________.