The pair of straight lines represented by the equation $\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0$ are

The equation of the circle concentric with circle $x^2 + y^2 - 6x + 7 = 0$ and which touches the line $x + y + 3 = 0$ is ....

The distance of the focus of the parabola $y^2 = 16x$ from its directrix is...

The value of $\lim_{n\to\infty} \dfrac{(n+2)! + (n+1)!}{(n+2)! - (n+1)!}$ is ____