The eccentricity of a rectangular hyperbola is:

If $(a - 2)x^2 + ay^2 = 4$ represents a rectangular hyperbola,then $a$ equals:

If the equation of one asymptote of the hyperbola $14 x^2+38 x y+20 y^2+x-7 y-91=0$ is $7 x+5 y-3=0$,then the other asymptote is

The locus of a variable point whose chord of contact with respect to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ subtends a right angle at the origin is

$A$ point moves in such a way that the difference of its distances from two points $(8,0)$ and $(-8,0)$ always remains $4$. Then, the locus of the point is

Let $A(\sec \theta, 2 \tan \theta)$ and $B(\sec \phi, 2 \tan \phi)$,where $\theta+\phi=\pi/2$,be two points on the hyperbola $2x^2-y^2=2$. If $(\alpha, \beta)$ is the point of intersection of the normals to the hyperbola at $A$ and $B$,then $(2\beta)^2$ is equal to ..... .