The equation of the pair of asymptotes of the hyperbola $x^2-2 y^2-8 x+8 y+4=0$ is

The equation of the hyperbola referred to the coordinate axes as axes of symmetry,whose distance between the foci is $16$ and eccentricity is $\sqrt{2}$,is

Let $x+y+1=0$ and $x-y+4=0$ be the asymptotes of a hyperbola $H$. If $(1,1)$ is a point on $H$,then the length of the latus rectum of $H$ is

The eccentricity of the hyperbola $x^2 - y^2 = 25$ is

If the tangent at the point $(2 \sec \phi, 3 \tan \phi)$ of the hyperbola $\frac{x^2}{4} - \frac{y^2}{9} = 1$ is parallel to $3x - y + 4 = 0$,then the value of $\phi$ is ............ $^o$.

The straight line $x + y = \sqrt{2}p$ will touch the hyperbola $4x^2 - 9y^2 = 36$,if