x^2+2hxy+by^2+2gx+2fy+c=0, depends upon a, b, c,h,g,f
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We can clearly see the black graph, it represents a conic section passing through five points A, B, C, D and E.
As we change the positions of the five points (A, B, C, D and E), the shape of this conic section changes and it becomes a circle, a parabola, an ellipse or a hyperbola.