Suppose image planes are in z = 1 plane.
Focal points are on y = 0, z = 0 line.
Any plane containing focal points has form:
Ax + By + Cz + D = 0, with A = 0, D=0, since any point with y = 0 and z = 0 satisfies this equation.
Specifically, we could say focal points are (0,0,0) (10,0,0).  Then (0,0,0)*(A,B,C) + D = 0, so D = 0.  (10,0,0)*(A,B,C) + D = 10A = 0  so A = 0.
So all planes through focal points have equation By + Cz = 0.  If we look at where these intersect the image planes (z=1) it’s at: By + C = 0.  These are horizontal lines.