Equation of Ellipse
Algebra
Level
5
There is an ellipse with focal points
\[P = (4, 2)\]
and
\[Q = (2, 4)\]
One of the points on the ellipse is \((2, 2)\). If the equation for this ellipse is
\[ax^2 + bxy + cy^2 + dx + ey + f = 0\]
where \(\gcd(a, b, c, d, e, f) = 1\) find the maximum value of the following expression:
\[a + b + c + d + e + f\]
by
Sharky Kesa