My 400 day Streak problem!

Geometry Level 5

\[K = (-10,13), U = (3,0),N = (-13,64),A = (9,8), L = (0,-1)\]

Consider the given points above on \(x\) and \(y\) plane.

An ellipse pass through above points whose equation can be written as \[ ax^2 + by^2 +cxy + dx +ey +f =0 \]

Where \( a,b,c,d,e,f\) are all integers and \(\text{GCD} (a,b,c,d,e,f) = 1 \)

Find the value of \( |a| + |b|+|c|+|d|+|e|+|f| \).

Inspired from this problem.

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