Properties of Hyperbola

What is Hyperbola?

A hyperbola is the locus of points whose difference in the distances from two foci is a fixed value. This difference is obtained by subtracting the distance of the nearer focus from the distance of the farther focus....

Hyperbola Equation

The equation of a hyperbola in its standard form depends on its orientation and whether it’s centered at the origin or another point. Here are the two primary forms for hyperbolas centered at the origin, one opening horizontally and the other opening vertically:...

Parts of Hyperbola

A hyperbola is a conic section that is developed when a plane cuts a double right circular cone at an angle such that both halves of the cone are joined. It can be described using concepts like foci, directrix, latus rectum, and eccentricity....

Hyperbola Eccentricity

The eccentricity of a hyperbola is the ratio of the distance of a point from the focus to its perpendicular distance from the directrix. It is denoted by the letter ‘e‘....

Standard Equation of Hyperbola

The standard equations of a hyperbola are:...

Latus Rectum of Hyperbola

Latus rectum of a hyperbola is a line passing through any of the foci of a hyperbola and perpendicular to the transverse axis of the hyperbola. The endpoints of a latus rectum lie on the hyperbola, and its length is 2b2/a....

Derivation of Hyperbola Equation

Let us consider a point P on the hyperbola whose coordinates are (x, y). From the definition of the hyperbola, we know that the difference between the distance of point P from the two foci F and F’ is 2a, i.e., PF’-PF = 2a....

Hyperbola Formula

Following hyperbola formulas are widely used in finding the various parameters of the hyperbola which include, the equation of hyperbola, the major and minor axis, eccentricity, asymptotes, vertex, foci, and semi-latus rectum....

Graph of Hyperbola

Hyperbola is a curve which has two unbounded curves which are mirror images of each other. The graph of the hyperbola shows that curve in the 2-D plane. We can observe the different parts of a hyperbola in the hyperbola graphs for standard equations given below:...

Conjugate Hyperbola

Conjugate Hyperbola are 2 hyperbolas such that the transverse and conjugate axes of one hyperbola are the conjugate and transverse axis of the other hyperbola respectively....

Properties of Hyperbola

If the eccentricities of the hyperbola and its conjugate are e1, and e2 then,...

Rectangular Hyperbola

A hyperbola with a transverse axis of 2a units and a conjugate axis of 2b units of equal length is called the Rectangular Hyperbola. i.e. in rectangular hyperbola,...

Parametric Representation of Hyperbola

Parametric Representation of auxiliary circles of the hyperbola is:...

Hyperbola Class 11

In Class 11 mathematics, the study of hyperbolas forms a part of the conic sections in analytic geometry. Understanding hyperbolas at this level involves exploring their definition, standard equations, properties, and various elements associated with them....

Summary – Hyperbola

A hyperbola is a type of conic section that forms when a plane intersects a cone at an angle such that two separate curves are produced. Characterized by its mirror symmetry, a hyperbola consists of two disconnected branches, each curving away from the other. It can be defined mathematically in a coordinate plane using a standard equation, which varies based on its orientation—either horizontal or vertical—and whether its center is at the origin or another point....

Solved Examples on Hyperbola

Question 1: Determine the eccentricity of the hyperbola x2/64 – y2/36 = 1....

Practice Problems on Hyperbola

P1. Find the standard form equation of the hyperbola with vertices at (-3, 2) and (1, 2), and a focal length of 5....

Hyperbola – FAQs

What is Hyperbola in Maths?...