Difference between Parabola and Hyperbola

The section of the cone that is created when a plane cuts a conical surface parallel to the side of the cone is known as a parabola. Similarly, the conic section created when a plane cuts the cone parallel to its axis is known as a hyperbola. Parabola and hyperbola are different in size, shape and various other factors including the formulas that are used to calculate it.

Parabola vs Hyperbola

Parabola Hyperbola
When a set of points in a plane are equidistant from a given directrix or a straight line and from the focus then it is called a parabola. When the difference of distances between a set of points present in a plane to two fixed points is a positive constant, it is called a hyperbola.
All parabolas are of the same shape irrespective of the size All hyperbolas are of different shapes
The two arms in a parabola become parallel to each other They do not become parallel