We have a directrix and we have a focal point. What's missing?

Algebra Level 5

There is a parabola with directrix defined by the line

\[3x + 7y = 21\]

and focal point

\[P = (3, 3)\]

The equation of the parabola can be written as

\[ax^2 + bxy + cy^2 + dx + ey + f = 0\]

where the \(\gcd(|a|, |b|, |c|, |d|, |e|, |f|) = 1\). Find the maximum value of

\[a + b + c + d + e + f\]

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