The equation of the plane passing through the points $(1, 2, -3)$ and $(2, -2, 1)$ and parallel to the $X$-axis is:

The Cartesian equation of the plane passing through the point $A(7,8,6)$ and parallel to the $XY$ plane is

The equation of a plane parallel to the plane $x - 2y + 2z - 5 = 0$ and at a unit distance from the origin is:

The mirror image of the point $P(-1, 2, -4)$ in the plane $x - y - 2z + 1 = 0$ is

Let the plane $\pi$ pass through the point $(1,0,1)$ and be perpendicular to the planes $2x+3y-z=2$ and $x-y+2z=1$. Let the equation of the plane passing through the point $(11,7,5)$ and parallel to the plane $\pi$ be $ax+by-z-d=0$. Then,$\frac{a}{b}+\frac{b}{d}=$

The equation of the plane passing through the points $(2,3,1)$ and $(4,-5,3)$ and parallel to the $y$-axis is: