The triangle has the largest area, that is, the distance between straight lines is the largest.

Let the straight line passing through p and parallel to AG be m.

Because the two straight lines are parallel,

The k value of m is the same as that of AG.

When the distance is maximum, there is only one intersection point between m and parabola.

The analytical formula of m is calculated by △ (b 2-4ac) = 0.

Then they all came out.

All by hand! ! ! !

I'm not bad at math, so I should be able to understand it.