The eccentricity of the hyperbola conjugate to the hyperbola $\frac{x^2}{4} - \frac{y^2}{12} = 1$ is

Let $H_{n} = \frac{x^2}{1+n} - \frac{y^2}{3+n} = 1$,where $n \in N$. Let $k$ be the smallest even value of $n$ such that the eccentricity of $H_{k}$ is a rational number. If $l$ is the length of the latus rectum of $H_{k}$,then $21l$ is equal to $.......$.

Let $e$ be the eccentricity of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$. If $\frac{1}{e}$ is the eccentricity of a hyperbola,then the eccentricity of its conjugate hyperbola is

If the line $\alpha x+2y=1$,where $\alpha \in \mathbb{R}$,does not meet the hyperbola $x^{2}-9y^{2}=9$,then a possible value of $\alpha$ is:

If the vertices of a hyperbola are at $(-2, 0)$ and $(2, 0)$ and one of its foci is at $(-3, 0)$,then which one of the following points does not lie on this hyperbola?

If the line $5x - 2y - 6 = 0$ is a tangent to the hyperbola $5x^2 - ky^2 = 12$,then the equation of the normal to this hyperbola at the point $(\sqrt{6}, p)$ where $p < 0$ is: