Difference between Parabola and Hyperbola

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.

Parabola: 

• A parabola is defined as a set of points in a plane which are equidistant from a straight line or directrix and focus.
• A parabola has single focus and directrix
• Eccentricity, e = 1
• All parabolas should have the same shape irrespective of the size
• The two arms present in a parabola should be parallel to each other
• It has no asymptotes

Hyperbola: 

• 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 hyperbola has two foci and two directrices
• Eccentricity, e>1
• The hyperbolas can be of different shapes
• The arms present in hyperbola are not parallel to each other.
• It has two asymptotes