If the angle between the asymptotes of the hyperbola $x^2-k y^2=3$ is $\frac{\pi}{3}$ and $e$ is its eccentricity,then the pole of the line $x+y-1=0$ with respect to this hyperbola is

Let $a>0, b>0$. Let $e$ and $\ell$ respectively be the eccentricity and length of the latus rectum of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$. Let $e^{\prime}$ and $\ell^{\prime}$ respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If $e^{2}=\frac{11}{14} \ell$ and $(e^{\prime})^{2}=\frac{11}{8} \ell^{\prime}$,then the value of $77a+44b$ is equal to

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 locus of the point of intersection of the tangents at the endpoints of normal chords of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is

The eccentricity of the hyperbola which passes through the points $(3,0)$ and $(3\sqrt{2}, 2)$ is

If the angle between the asymptotes of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{3} = 4$ is $\frac{\pi}{3}$,then its conjugate hyperbola is: