I have seen a statement in a text book which is given as a passing reference. It says that diametral plane of surface $f(x,y,z) = 0$ is given as $l\frac{df}{dx}+m\frac{df}{dy}+n\frac{df}{dz} = 0 $ in direction of $l,m,n$ - system of parallel chords.
Given a conicoid - $ax^2+by^2+cz^2 = 0 $ and system of parallel chords in direction $l,m,n$ I can derive diametral plane as $alx+bmy+cnz = 0 $ by taking the mid-point and general equation of the line and making sum of roots $= 0$.
But how to prove diametral equation form (1) ...Any idea Pls?