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# Difference between Parabola and Hyperbola

## Definition of Parabola and Hyperbola

A parabola is a symmetrical U-shaped curve. It is created by the intersection of a plane with a cone when the plane is parallel to one of the cone’s sides. In mathematics, a parabola is defined as the set of all points in a plane that are equidistant from a fixed point and a fixed-line.

A hyperbola is a symmetrical curve. It is created by the intersection of a plane with a double cone. In mathematics, a hyperbola is the set of all points in a plane such that the difference between the distances to two fixed points is constant. The two branches of a hyperbola are mirror images of each other. They are asymptotic to two lines called asymptotes. ## What is the difference between Parabola and Hyperbola?

The main difference between a parabola and a hyperbola is their shape and the way they are explain.

Parabola Hyperbola
Shape U-shaped curve Symmetrical curve with two branches
Formation Intersection of a plane with a cone parallel to one of its sides Intersection of a plane with a double cone
Definition All points on the curve are equidistant from a fixed point (focus) and a fixed line (directrix) All points on the curve have a constant difference between the distances to two fixed points (foci)
Foci and Asymptotes One focus and one directrix Two foci and two asymptotes
Symmetry Symmetric with respect to its axis of symmetry, which is perpendicular to its directrix Symmetric with respect to its center
Equation y = ax^2 or x = ay^2 (x – h)^2/a^2 – (y – k)^2/b^2 = 1 or (y – k)^2/a^2 – (x – h)^2/b^2 = 1

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