$x+y+3=0,2 x-y+1=0$ are the equations of the asymptotes of a hyperbola.

If $(1,-2)$ is a point on this hyperbola, then the equation of its conjugate hyperbola is

If $\theta$ is the acute angle between the tangents drawn from the point $(1,1)$ to the hyperbola $4 x^2-5 y^2-20=0$, then $\tan \theta=$

If the equation of the tangent of the hyperbola $5 x^2-9 y^2-20 x-18 y-34=0$ which makes an angle $45^{\circ}$ with the positive $X$-axis in positive direction is $x+b y+c=0$, then $b^2+c^2=$

If the distance between the foci of a hyperbola $H$ is 26 and distance between its directrices is $\frac{50}{13}$, then the eccentricity of the conjugate hyperbola of the hyperbola $H$ is