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.
|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|