Find ellipse area

A "potential" ellipse is described by the coefficients of its quadratic equation.
a x^2 + b xy + c y^2 + d x + e y + f = 0
the vector of coefficients, [a, b, c, d, e, f] should be used as the input.

For example, for a circle, x^2 + y^2 - 1 =0, the input should be [1 0 1 0 0 -1]. And find_ellipse_area([1 0 1 0 0 -1]) will return pi, the area of the circle.

If the quadratic equation doesn't represent an eclipse (for example, a hyperbola, instead), the function will return NaN.