The eccentricity of an ellipse passing through $(3 \sqrt{2}, \sqrt{10})$ with foci at $(-4,0)$ and $(4,0)$ is

If the product of the lengths of the perpendiculars drawn from the foci to the tangent $y=\frac{-3}{4} x+3 \sqrt{2}$ of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is 9 , then the eccentricity of that ellipse is

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

If the points $A(-1,0,7), B(3,2, t), C(5, k,-2)$ are collinear, then the ratio in which the point $P(t, k-2 t, t+k)$ divides the line segment $B C$ is