let, ax^2 + by^2 + 2hxy + 2gx + 2fy + c = 0, then we know (i) if a=b and h=0 the conic is a circle (ii) if h^2ab the conic is in general a hyperbola except when the determinant |a h g| |h b f| = 0, when it is a line pair. |g f c| (iv) if a+b = 0, and in consequence h^2ab, the conic is a rectangular hyperbola (or a perpendicular line pair if above determinant = 0). (v) if h^2 = ab, the conic is in general a parabola. Does anyone know how to derive

Question

let, ax^2 + by^2 + 2hxy + 2gx + 2fy + c = 0,

then we know
(i) if a=b and h=0 the conic is a circle

(ii) if h^2<ab the conic is an ellipse with the exception of the 
special case (i).

(iii) if h^2>ab the conic is in general a hyperbola except when the 
determinant
            |a h g|
            |h b f| = 0, when it is a line pair.
            |g f c|

(iv) if a+b = 0, and in consequence h^2>ab, the conic is a rectangular 
hyperbola (or a perpendicular line pair if above determinant = 0).

(v) if h^2 = ab, the conic is in general a parabola.

Does anyone know how to derive

anonymous · Answer

What do you want to derive?

anonymous · Answer

if h^2 = ab then the given curve is a parabola