Difference between Parabola and Hyperbola

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The major difference between parabola and hyperbola is based on their eccentricity. For parabola, eccentricity is equal to 1, and for hyperbola, eccentricity is greater than 1. Although both are part of conic sections, there are other differences too, which separates parabola and hyperbola from each other. See the graph below to understand the differences.

Definition of Parabola and Hyperbola

The section of the cone called parabola is formed if a plane (flat surface) divides the conical surface, which presents parallel to the side of the cone.

Similarly, the conic section called hyperbola is formed when a plane divides the cone parallel to its axis.

Both the conic sections, parabola and hyperbola, are different in size, shape and other different criteria, including the formulas that are employed to determine it. In this article, let us understand how is a parabola difference from a hyperbola.

What is the difference between Parabola and Hyperbola?

Parabola	Hyperbola
A parabola is defined as a set of points in a plane which are equidistant from a straight line or directrix and focus.	The hyperbola can be defined as the difference of distances between a set of points, which are present in a plane to two fixed points is a positive constant.
A parabola has single focus and directrix	A hyperbola has two foci and two directrices
Eccentricity, e = 1	Eccentricity, e>1
All parabolas should have the same shape irrespective of the size	The hyperbolas can be of different shapes
The two arms present in a parabola should be parallel to each other	The arms present in hyperbola are not parallel to each other.
It has no asymptotes	It has two asymptotes

Both hyperbolas and parabolas are open curves; in other words, the curve of parabola and hyperbola does not end. It continues to infinity. But in case of the circle and ellipse, the curves are closed curves.

Frequently Asked Questions – FAQs

What is a Parabola?

Parabola is the locus of all points which are equally spaced from a fixed line (called directrix) and a fixed point (called the focus).

What is hyperbola?

A hyperbola is the locus of all those points in a plane where the difference in their distances from two fixed points in the plane is constant. It has two foci and directrices.

What are the four conic sections?

The four conic sections are:
Circle
Ellipse
Parabola
Hyperbola

What is the equation of parabola?

The equation of parabola whose focus is at x-axis (a,0) and a>0 is given by:
y² = 4ax

What is the equation of hyperbola?

The equation of the hyperbola is given by;
(x²/a²) – (y²/b²) = 1