## Difference Between Parabola and Hyperbola

**Parabola vs Hyperbola**

Parabola and hyperbola are two different sections of a cone. We can deal with their differences in a mathematical explanation or deal with the differences in a very simple way which not only mathematicians but everybody can understand. This article will try to explain the difference between them in a very simple way.

First of all, when a solid figure, which in this case is a cone, is cut by a plane, the section which is obtained is called a conic section. Conic sections could be circles, ellipses, hyperbolas, and parabolas depending upon the angle of intersection between axis of the cone and the plane. Both parabolas and hyperbolas are an open curve which means that the arms or branches of the curves continue to infinity; they are not closed curves like a circle or an ellipse.

**Parabola**

A parabola is the curve obtained when the plane cuts parallel to the cone side. In a parabola, a line passing through the focus and perpendicular to the directrix is called an “axis of symmetry.” When the parabola is intersected by the point on the “axis of symmetry,” it is referred to as the “vertex.” All parabolas are shaped identically as they are cut at a specific angle. It is a characterized by the eccentricity of “1.” This is the reason why they are all the same shape but can be of different sizes.

The parabola is given by the equation y2=X

When a set of points present in a plane are equidistant from the directrix, a given straight line, and are equidistant from the focus, a given point which is fixed, it is called a parabola.

Parabolas have many practical applications. They are used for designing the path of missiles, headlight reflectors of automobiles, telescopes, radar receivers, and satellite dishes.

**Hyperbola**

Hyperbola is the curve obtained when the plane cuts almost parallel to the axis. Hyperbolas are not identical in shape as there are many angles between the axis and the plane. “Vertices” are the points on the two arms which are closest; whereas the line segment which connects the arms is called the “major axis.”

In a parabola, the two arms of the curve, also called branches, become parallel to each other. In a hyperbola, the two arms or curves do not become parallel. A hyperbola’s center is the midpoint of the major axis.

Hyperbola is given by the equation XY=1

When the difference of distances between a set of points present in a plane to two fixed foci or points is a positive constant, it is called a hyperbola.

Summary:

When a set of points present in a plane are equidistant from the directrix, a given straight line, and are equidistant from the focus, a given point which is fixed, it is called a parabola. When the difference of distances between a set of points present in a plane to two fixed foci or points is a positive constant, it is called a hyperbola.

All parabolas are of the same shape no matter what the size; all hyperbolas are of different shapes

The parabola is given by the equation y2=X; a hyperbola is given by the equation XY=1

In a parabola the two arms become parallel to each other whereas in a hyperbola they do not.

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“a very simple way which not only mathematicians but everybody can understand”…

…”In a parabola, a line passing through the focus and perpendicular to the directrix is called an “axis of symmetry.”

Hmmm…

“When a set of points present in a plane are equidistant from the directrix, a given straight line, and are equidistant from the focus, a given point which is fixed, it is called a parabola.”

Phew – This is hard work…

Interesting though, thanks

Wait what? The arms of the function fx=x^2 become parallel? That would imply that fx is defined on a finite domain.