The distance between the foci of the hyperbola $x^2 - 3y^2 - 4x - 6y - 11 = 0$ is

Let the foci and length of the latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ be $(\pm 5, 0)$ and $\sqrt{50}$,respectively. Then,the square of the eccentricity of the hyperbola $\frac{x^2}{b^2}-\frac{y^2}{a^2b^2}=1$ equals

The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is

The eccentricity $e$ of a hyperbola can never be equal to which of the following values?

If the variable line $y = kx + 2h$ is tangent to an ellipse $2x^2 + 3y^2 = 6$,the locus of $P(h, k)$ is a conic $C$ whose eccentricity equals

The angle between the tangents drawn from the point $(2\sqrt{2}, 1)$ to the hyperbola $16x^2 - 25y^2 = 400$ is ........