In general quadratic form, an ellipse is described by 6-coefficients: F(x,y) = a*x^2 + 2*b*x*y + c*y^2 + 2*d*x + 2*e*y + f = 0 a*c - b*b > 0
where [a,b,c,d,e,f] are the coefficients and [x,y] is the coordinate of a point on the ellipse.

In general quadratic form, an ellipse is described by 6-coefficients: F(x,y) = a*x^2 + 2*b*x*y + c*y^2 + 2*d*x + 2*e*y + f = 0 a*c - b*b > 0
where [a,b,c,d,e,f] are the coefficients and [x,y] is the coordinate of a point on the ellipse.

An ellipse described using its center, semi-axes, and orientation.
(x'*cos(phi) + y'*sin(phi))^2/a^2 + (-x'*sin(phi) + y'*cos(phi))^2/b_2 = 1
x' = x-x_0, y' = y-y_0
where (x_0,y_0) is the center, (a,b) are major and minor axises, and phi is it's orientation.

An ellipse described using its center, semi-axes, and orientation.
(x'*cos(phi) + y'*sin(phi))^2/a^2 + (-x'*sin(phi) + y'*cos(phi))^2/b_2 = 1
x' = x-x_0, y' = y-y_0
where (x_0,y_0) is the center, (a,b) are major and minor axises, and phi is it's orientation.