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