Is it a Circle?

Calculus Level 5

An ellipse passes through the points (0,1)(0,-1), (2,0)(2,0), and (2,2)(-2,2) and encloses minimum possible area.

Ax2+Bxy+Cy2+Dx+Ey+F=0Ax^2+Bxy+Cy^2+Dx+Ey+F=0 is the equation representing the ellipse, where AA and BB are positive coprime integers.

Find A+B+C+D+E+FA+B+C+D+E+F.

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