Why is it called a rectangular hyperbola?

Open in App

Solution

Rectangular Hyperbola:
A rectangular hyperbola has its asymptotes or axes perpendicular to each other.
The length of the transverse axis is equal to the length of the conjugate axis.
The general form of a regular hyperbola is $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ . For a rectangular hyperbola, the value of $a = b$ .
The general equation of a rectangular hyperbola is $x^{2} - y^{2} = a^{2} o r x^{2} - y^{2} = b^{2}$

Since the asymptotes of a rectangular hyperbola are perpendicular to each other, that's why it is known as a rectangular hyperbola.

Suggest Corrections

Similar questions

Q. Assertion :A hyperbola whose asymptotes are at right angles to each other is called rectangular hyperbola. Reason: Eccentricity of rectangular hyperbola is

\sqrt{2}

Q. Define Rectangular Hyperbola and find its eccentricity

Q. If a triangle is inscribed in a rectangular hyperbola,its orthocentre lies

Which of the following statements are correct?

1. The particular kind of hyperbola in which the lengths of the transverse and conjugate axis are equal is called an equilateral hyperbola.

2. Eccentricity of equilateral hyperbola = $\sqrt{2}$
3. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = 0$

4. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = - a^{2}$

Q. When data is represented using rectangular bars, it is called a ______ .

Join BYJU'S Learning Program