# There are enough points, but how do you determine the equation?

Algebra Level 5

There is a hyberbola that passes through points

$A = (0, 6)$

$B = (1, 3)$

$C = (3, 1)$

$D = (6, 0)$

$E = (10, -1)$

If the equation for this hyperbola can be represented as

$ax^2 + by^2 + cxy + dx + ey + f = 0$

where the $$\gcd (a, b, c, d, e, f)$$ is 1, find the minimum value of

$a + b + c + d + e + f$

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