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There is an ellipse with focal points
P=(4,2)P = (4, 2)P=(4,2)
and
Q=(2,4)Q = (2, 4)Q=(2,4)
One of the points on the ellipse is (2,2)(2, 2)(2,2). If the equation for this ellipse is
ax2+bxy+cy2+dx+ey+f=0ax^2 + bxy + cy^2 + dx + ey + f = 0ax2+bxy+cy2+dx+ey+f=0
where gcd(a,b,c,d,e,f)=1\gcd(a, b, c, d, e, f) = 1gcd(a,b,c,d,e,f)=1 find the maximum value of the following expression:
a+b+c+d+e+fa + b + c + d + e + fa+b+c+d+e+f
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