If $(8,2)$ is a point on the hyperbola whose length of the transverse axis is 12 and conjugate axis is $x=0$, then the eccentricity of that hyperbola is

A rectangular hyperbola passing through $(3,2)$ has its asymptotes parallel to the coordinate axes. If $(1,1)$ is the point of intersection of the two perpendicular tangents of that hyperbola, then its equation is

If the circle $x^2+y^2=a^2$ intersects the hyperbola $x y=b^2$ at four points $\left(x_1, y_1\right),\left(x_2, y_2\right),\left(x_3, y_3\right),\left(x_4, y_4\right)$, then $y_1 \quad y_2 \quad y_3 y_4=$

The equation of the hyperbola, whose eccentricity is $\sqrt{2}$ and whose foci are 16 units apart, is