## 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 |