Hyperbola Formula

Hyperbola Foci Formula

The line segment across the foci is known as the transverse axis. Also, the line segment through the midpoint and perpendicular to the transverse axis is known as the conjugate axis. The points at which the hyperbola bisects the transverse axis are referred to as the vertices of the hyperbola.

  • The distance between the two foci is: 2c

  • The length of the conjugate axis is 2b… in which b = √ (c2 – a2)

  • The distance between two vertices is: 2a (i.e. also the length of the transverse axis)

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Equation of Hyperbola 

The hyperbola equation is,

(x−x0) 2/a2 – (y-y0) 2/b2 = 1

Where,

x0, y0 = The center points.

a = Semi-major axis.

b = Semi-minor axis.


All Formula of Hyperbola

Let’s refer to the hyperbola formula table and learn the basic terminologies with respect to the hyperbola formula:

  1. Minor Axis

The line perpendicular to the major axis and crosses through the centre of the hyperbola is the Minor Axis.

The length of the minor axis is 2b. The equation is as follows:

x = x0

  1. Major Axis

The line that crosses by the middle, the focus of the hyperbola and vertices is the Major Axis. The length of the major axis is 2a. The equation is as follows:

y = y0

  1. Eccentricity

The differentiation in the conic section being fully circular is eccentricity. It is generally higher than 1 for hyperbola. Eccentricity is 2√2 for a regular hyperbola. The eccentricity formula is:

\[\frac{\sqrt{a^{2}+b^{2}}}{a}\]

  1. Asymptotes

Two intersecting line segments that are crossing through the centre of the hyperbola which does not touch the curve are called the Asymptotes. The asymptotes formula is given as:

y = y0 + b/ax – b/ax0

y = y0 − b/ax + b/ax0


Directrix of Hyperbola

The directrix of a hyperbola is a straight line that is used in incorporating a curve. It can also be described as the line segment from which the hyperbola curves away. This line segment is perpendicular to the axis of symmetry. The equation of directrix formula is as follows:

x = \[\frac{ a^{2}}{\sqrt{a^{2}+ b^{2}}}\]

FAQs (Frequently Asked Questions)

Q1. What is a Hyperbola?

Answer: Simply to say, a hyperbola appears identical to the mirrored parabolas. The two halves are called the branches. When the plane bisects on the halves of a right circular cone angle of which is parallel to the axis of the cone, then hyperbola is created. 

Q2. What is Meant by the Equation of Hyperbola?

Answer: The equation of Hyperbola is the set of all points in a plane system, the difference of whose distances in the plane is constant from two fixed points. ‘Difference’ refers to the distance to the ‘farther’ point minus the distance to the ‘closer’ point. The two fixed points are the foci and the midpoint of the line connecting the foci is the midpoint of the hyperbola.

Q3. What is the Latus Rectum of the Hyperbola?

Answer: Latus rectum of a hyperbola is basically a line perpendicular to the transverse axis via any of the foci and whose endpoints lie on the hyperbola. In a hyperbola, the length of the latus rectum is 2b2/a.