Rectangular Hyperbola Formulas
Some of the rectangular hyperbola formulas and equations are listed below
- Eccentricity of the rectangular hyperbola is √2.
- Asymptotes equation of the rectangular hyperbola is y = ±x or x2 – y2 = 0.
- Standard equation of the rectangular hyperbola is x2 – y2 = a2
- Parametric equation of the rectangular hyperbola is x = asecθ, y = atanθ
Eccentricity of Rectangular Hyperbola
The equation of rectangular hyperbola is, x2 – y2 = a2. Now we know that eccentricity of the hyperbola is,
e = √(1 + b2/a2)
In case of rectangular hyperbola, a = b = 1. Now,
e = √(1 + b2/a2) = √(1 + 1/1) =√(2)
Asymptotes of a Rectangular Hyperbola
Asymptote are the lines that connects the curve at infinity. In case of rectangular hyperbola the equation of asymptote is,
- y = ±x
- x2 – y2 = 0
Asymptotes of a Rectangular Hyperbola are Perpendicular.
Rectangular Hyperbola
Rectangular Hyperbola is a hyperbola in which the transverse and conjugate axes are equal. i.e. in the case of rectangular hyperbola a = b = 1. The asymptote of the rectangular hyperbola is y = ±x. Also, the asymptotes of a rectangular hyperbola are perpendicular.
In this article, we will explore the rectangular hyperbola in depth along with its standard equation, eccentricity, asymptotes, and parametric equation.
Table of Content
- What is a Rectangular Hyperbola?
- Rectangular Hyperbola Shape
- Rectangular Hyperbola Equation
- Parametric Equation of Rectangular Hyperbola
- Rectangular Hyperbola Graph
- Rectangular Hyperbola Formulas
- Properties of Rectangular Hyperbola
- IIT JEE Formulas for Rectangular Hyperbolas
- Examples on Rectangular Hyperbola
- Practice Questions on Rectangular Hyperbola
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