The implicit form is convenient for 2-D curves of 1st and 2nd order because it allows for a more compact and general representation of the curve. In the implicit form, the equation of the curve is expressed as a single equation involving both the x and y variables, whereas in the explicit form, the equations are separated into functions of x and y.
For curves of 1st and 2nd order, the implicit form allows for a more concise representation of the curve without having to explicitly solve for one variable in terms of the other. This can make it easier to analyze and manipulate the curve mathematically.
Additionally, the implicit form is often more suitable for handling curves with complex or irregular shapes, as it can account for singular points, multiple branches, and self-intersections more effectively than the explicit form.
Overall, the implicit form is convenient for 2-D curves of 1st and 2nd order due to its compactness, generality, and ability to handle complex curves more efficiently.
