Math for max and min x and y of an ellipse I see that the general equation of an ellipse centered at the origin is:
   (+)² + (+)² = ²
How do a, b, c, d relate to the coefficients of the general form?
   A² + B + C² + D + E + F = 0
After some naive observation I believe:
   A = (² + ²)
   B = 2( + )
   C = (² + ²)
   F = -²
Pretty sure it's more complicated than that. The issue for me is to do the calculations based on numerical values for an ellipse in either standard or canonical form, as opposed to pencil and paper derivatives.

$$(ax+by)^2+(cx+dy)^2=r^2\\
a^2x^2+2abxy+b^2y^2+c^2x^2+2cdxy+d^2y^2=r^2\\
(a^2+c^2)x^2+(2ab+2cd)xy+(b^2+d^2)y^2-r^2=0\\
\therefore A=a^2+c^2B=2(ab+cd),C=(b^2+d^2),D=E=0,F=-r^2$$
