If the angle made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with X-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

The equation of a circle whose center lies on $x + 2y = 0$ and touching the lines $3x - 4y + 8 = 0$ and $3x - 4y - 28 = 0$ is

If $P$ be any point on the ellipse $16x^2 + 25y^2 = 400$ with foci $S$ and $S'$ and area of $\triangle PSS'$ is 9 square units, then the abscissa of point $P$ is...........

The value of $\lim\limits_{n \to \infty}\left[\dfrac{1}{1 - n^2} + \dfrac{2}{1 - n^2} + \ldots + \dfrac{n}{1 - n^2}\right]^3$ is