Difference Between Parabola and Hyperbola
When the question of reducing the equation of the curve to a canonical form arises, the rule refers to the curves of the second order illustrating whether it is an ellipse, parabola or hyperbola.
Compare the total equation of each of the canonical. It is easy to conclude that if the coefficients A ≠ 0, C ≠ 0, and the sign is the same, after any transformation, leading to the canonical form will be received by an ellipse. If the sign is different, it is hyperbola. Parabola will also be appropriate to the situation, or when the coefficients A and C (but not both) are zero. Thus, there is no numerical characteristics, except those factors that are specific to the problem statement.
We restrict ourselves to the ellipse (mostly) and hyperbole. Parabola occurs automatically, as is the case in between. The fact that the original ellipse is defined as the locus of points for which the sum of the focal radii r1 + r2 = 2a = const. For the hyperbola  r1r2  = 2a = const. Place the foci of the ellipse (hyperbola) F1 (c, 0), F2 (c, 0). Then the focal radii of the ellipse are equal.
Graphically, hyperbole contains two smooth curved lines. Each of them flips another relatively early point of Cartesian coordinates. If the function y = k / x, has a coefficient of k – is greater than zero, then the hyperbola will be placed in the first and third quarters. In this case, the function is decreasing on the entire domain, which consists of two intervals: ( ∞; 0) and (0; + ∞). Build the first branch of the hyperbola on (0; + ∞). Find the coordinates of the points needed to construct the curve. To do this, set the variable x some arbitrary values, and the values of the variable y. Build a second curve of the hyperbola in the interval ( ∞; 0). Put points on the coordinate plane and connect them by a smooth line, than form two symmetrical curves relative to the point of intersection of the axes.
Instructions

1
Hyperbola:
A hyperbola consists of two disconnected curves called connected components and contains a smooth curve that lies within a plane. 
2
Parabola:
Hyperbola is somewhat similar to parabola as both are an open curve and continue indefinitely to infinity unlike ellipse. However, they can be differentiated through set of equations. Parabola is a conic section containing the intersection of a right circular conical surface.