Parabola and hyperbola with tabular form

The main difference between parabola and hyperbola is based on their eccentricity. For the parabola, the eccentricity is equal to 1, and for the hyperbola, the eccentricity is greater than 1. Parabola and hyperbola with tabular form

Although both forms are part of conic sections, there are also other differences, which separate the parabola and the hyperbola from each other. See the chart below to understand the differences.

Definition of parable and hyperbola Parabola and hyperbola with tabular form

Before entering to address the differences between these two geometric shapes. Let us remember that it is each one of them.

The section of the cone called the parabola is formed if a plane (flat surface) divides the conical surface, which is parallel to the side of the cone.

Similarly, the conic section called the hyperbola is formed when a plane divides the cone parallel to its axis.

Both the conic sections, parabola and hyperbola, are different in size, shape and other different criteria, including the formulas used to determine it. In this article, let’s understand how a parable differs from a hyperbola.

What is the difference between a parable and a hyperbola? Parabola and hyperbola with tabular form

Parable Hyperbola
A parabola is defined as a set of points in a plane that are equidistant from a straight line or directrix and focus. The hyperbola can be defined as the difference in distances between a set of points, which are present in a plane at two fixed points, it is a positive constant.
A parabola has a single focus and directrix A hyperbola has two focuses and two guidelines
Eccentricity, e = 1 Eccentricity, e> 1
All parabolas must have the same shape regardless of size. Hyperbolas can have different shapes.
The two arms present in a parabola must be parallel to each other. The arms present in the hyperbola are not parallel to each other.
It has no asymptotes It has two asymptotes

Both hyperbolas and parabolas are open curves; in other words, the parabola and hyperbola curve does not end. It continues to infinity. But in the case of the circle and the ellipse, the curves are closed curves.

Frequently asked questions about parables and hyperbolas Parabola and hyperbola with tabular form

What is a parable?

The parabola is the locus of all points that are equally spaced between a fixed line (called a directrix) and a fixed point (called a focus).

What is hyperbola?

A hyperbola is the locus of all those points in a plane where the difference in their distances from two fixed points in the plane is constant. It has two focuses and guidelines.

What are the four conic sections?

The four conic sections are:

  • Circle
  • Ellipse
  • Parable
  • Hyperbola

What is the equation of the parabola?

The parabola equation whose focus is on the x-axis (a, 0) and a> 0 is given by:

  • and  2  = 4ax

What is the equation of the hyperbola?

The equation of the hyperbola is given by;

  • (x  2  / a  2  ) – (y  2  / b  2  ) = 1

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